From his efforts to pacify the old Anglo-Scottish borders, remove the administrative and legal systems that set them apart, and make them into his new 'Middle Shires', it seems that James VI intended England and Scotland to act as one joint kingdom under his rule. Is this an accurate understanding of his intentions and, if so, were any efforts made to unify the two kingdoms politically, perhaps under a single Parliament?
Yes, it's an accurate understanding, and yes, he did make an effort to effect a statutory unification of the two but his attempt was defeated in Parliament in April of 1607. Basically, neither England nor Scotland was ready for a political union at the time of James's accession to the English throne. Both sides were too jealous of their own rights and privileges and both sides exhibited an unsurprising level of xenophobic hostility to the notion of complete union. A nice overview to the Parliamentary defeat was given by Dr Andrew Thrush and can be heard here. For further reading on the topic from an admittedly Scottish standpoint, I'd suggest looking into the writings of Keith Brown, Maurice Lee, Jenny Wormald, and Julian Goodare.