That sounds like a great plan. Glad to hear that the brakes reach, sometimes this does happen. I really
think 700c alloy wheels are one of the most noticeable upgrades you can make. The lower rotating
mass and smaller diameter should give you payoff you can feel, and being the more common size,
opens up a lot of possibilities for different wheelsets. I have a set of Mavic Aksium race wheels
for my old Trek 560, they are better than the original Matrix, but I have kept all the original parts
in dry storage, so the preservation aspect of the vintage bike is doable.
As for the seven speeds... you probably have a freewheel system, while newer wheels are
usually built with freehubs and cassettes. So- new wheels will necessitate a new cassette,
which should get you 9 or 10 speeds. This would fit right in with the plan for derailleurs and
chain.
Glad to hear that the new ride is working out so well.