According to the book I'm reading, the Heads of Proposals were much more attractive to Charles I than the some of the initial settlement plans offered to him by Parliament. This seem confusing, because my understanding is that the Army was a more radical force than the Parliament insofar as it was full of Independent Protestants who opposed the Presbyterianism dominant in Westminster.
The main grievance of both parliament and the army was Laudianism, this was removed quite swiftly from 1641. Laudianism was a more ceremonial form of Anglican worship and was seen by many as 'papist'.
By the end of the Civil War Charles I had ditched William Laud and adopted Calvinism (at least publically). Between 1641-43 Charles I nominates 11 new bishops, all of whom were strict Calvinists or were enemies of Laud. William Laud himself is executed in 1645.
Calvinism (or at least in the form of Jacobean Anglicanism) was firmly established in England and outside of London and Parliament there was little call for its replacement with presbyterianism. In fact the erosion of the Jacobean Church is arguably what the Civil War was about (the last of the wars of the religion). Presbyterianism was unpopular with many people as it meant the rejection of the Anglican Prayer Book to which many had become attached, its Presbyterian replacement was unpopular with only 10% of parishes adopting it within the first 6 months of its introduction. Even in parishes where the new book was used the Anglican Prayer Book was still the prefered choice for Baptisms and Funerals. Even when a bishop was removed from power he was still seen by many as the legitimate power, for example between 1646-1654 fifty new ministers sought ordination with the Bishop of Norwich, despite the fact they were already ordained by Presbyterians.
so in answer to your question the reason the Heads of Proposals seemed less extreme is because there really wasn't too much demand for a radical puritan church, even in Parliament. Decisions bringing England down the road to Presbyterianism were often unpopular and unsuccessful, even within the clergy. In many ways the Puritan Revolution was a failure, the Puritan Campaign to reform worship was impossible to “enforce on a people who for the most part viewed it with a withering scorn and contempt, and defiantly refused to abandon their traditional practices.” (Durston).
Sources Durston, C. Culture of English Puritanism
Durston, C. & Maltby, J. Religion in Revolutionary England
McElligott and Smith Royalists and Royalism during the Interregnum
Coffey, T Persecution and Toleration in Protestant England