Reposting... third time's the charm?
Anyways, my vague sense of the period is that socio-cultural restraints were generally stronger on upper class women who were expected to be exemplars of their sex, so I'm certainly more interested in that slice, although I don't want to cut out any interesting angles that this question might cover within the lower segments of society.
My impression also is that the most easy way to have "independence" was to be a widow, probably with a young son who wasn't able to control his fortune himself. To be sure I'm also not cutting out them (although open to correction if I'm wrong there), but what I'm really interested is in those who aren't granted it by unfortunate (or fortunate?) circumstance. That is to say, a young woman raised in a good family, makes a fairly average marriage, and begins motherhood, or, of course, a woman from a good family who remains unmarried yet wants to do more than join a nunnery, or be an old maid in her father's house.
What avenues were available to women such as these to maintain a sense of self and control within the expectations of the society she lived in?
Well, I think it is a mistake to assume that Early Modern people expected or even necessarily wanted women to be lacking agency or action. it is more complicated.
Disclaimer this is based mostly on England which was noted by travellers as having unusually bold women, so some caveats apply.
The family was understood as a strategic grouping to which each member was expected to contribute, and family members of all sorts acted as agents to promote their families interests and sure-up marriage bonds with other families. And of course speaking of marriage, marriage we know was significantly strategic in terms of property ownership and that family ties element. So married women would be fairly expected to promote the interests of their own family, of their husband, of especially children, and they managed the household. That management would be from a more distant leadership position if they were aristocratic, more hands on if they are lower down, varying depending on how many servants there are to do the grunt work for them. Women also formed large social circles with each other (this society being homosocial, large same gender friend circles were expected) and these ties to other households could also be put to use, again in service of their family, their husband, their children and the management of their household. For aristocratic women a significant number served in the royal court household and these women could subtly promote their husband and family interests to the monarch, as well as serving as intermediaries between various court people's in the service of their husband as came up.
All of this is framed in the interests and under the direction of the husband and father but there is a lot of latitude for their own adult discretion which scholars increasingly recognise. Some Early Modern women also wrote poetry and other writings, and under Anne(Danish: Anna) of Denmark (James VI and I's consort) women performed in court masques including the Queen herself. Anne of Denmark is an interesting, and under-recognised, example of independent women because she took formal and personal control over her children by turning Scottish nobles to her side to convince her husband, and she also exerted influence over the choice of her household ladies; editing the list of approved ladies by introducing her own and refusing to accept some. While she was always forced to bow to James' wishes if he insisted, he was not uncommonly persuaded by her arguments and her stubbornness to make some concessions for her, and had to begrudgingly recognise her agency (Her complicated relationship with her husband is an interesting topic of it's own). She had her own gift of land with a court, the Queen's Court of Chancery, to administer it and she took petitions from interested parties. She also served as semi-official regent whenever James was hunting in the country with courtiers waiting on her and was appointed to his official Regency Council when he went to Scotland in 1617.
For a young girl who is unmarried while their marriages choices would be subject to the will of their parents, and others including neighbours, the actual level of control they exerted was variable. It was possible for relatives to recognise and consider the feelings of the woman; playing off the same strategy of turning norms to their own end she could argue her own case. And of course once they married a husband, which could not strictly be stopped by parents if done correctly, they were mostly independent from them, they could move neighbourhoods to get away from objecting neighbours and the husband can instead supply for them. Arguing their case to parents would help because parents supplied the dowry which was intended to help establish their new household and could be very beneficial, including houses and rent-paying lands even, in establishing their own finances.
A woman who remains unmarried is best off relying, if as you say not on her father, on other relatives and on female friend circles. Particularly in cunning folk circles; while marriage was still common, independent activity among those female circles was particularly rife, and involved magic and medicine, which are two reasons are why they were targeted heavily in witch hunts. A cunning folk woman without a house could live with one of her friends and co-practitioners who did have one, and practise together (side-note: doesn't that sound like a fabulous situation for lesbianism?). if you are from a good family you could always try to get enough money and/or property from your father to establish a household without a husband, but getting your husband would probably help convince him and the husband could help you earn money given the less profitable work opportunities for women in Early Modern society. Middle class women with enough inheritance to at least rent a room could take work making and selling various bits and bobs, common among lower and middle class women, and try and save enough money that way.
There is an interesting dynamic in Early Modern societies that is relevant here. High-class society has more power and room to bend the rules but more pressure to conform to standards. Rural society offers lower rewards with more vulnerability but also the possibility of looser living with the lower expectations (for example premarital sex was more commonly and openly accepted in rural towns). So there are two different paradigms with their own risks and rewards depending on whether one is more of a farm resident or a gentry or aristocrat woman.
So in conclusion Early Modern women who are not widows can exercise agency of behalf of men in their lives, much as widows derived their power from their sons. Marriages could involve the woman's wishes if her relatives are respectful enough and she is able to subtly make her case. Women who remained unmarried could draw on other relatives or female friend connections if they did not wish to remain with their father, and inheritance and work could be drawn upon to make your household if you were willing to take the risk. So while women were not allowed to gain the same power and independence as men, and were not usually able to access the same work opportunities, they could in-fact exert influence, make their will known, do work and even have had a household without father or husband. Context and methods are key.