I get there is little room inside, however, all new caps of the same value will be much smaller. At times I have had to check the values again, they are less then 1/2 the old caps size for the same value. In fact have gone up in voltage on a lot of caps, they are sill much smaller.
Point it, there should be a lot more room, after you swap out a few caps.
Yes, do not purchase any "kits" get the service manual, it should have a parts list, with that, put together an order with mouser or digikey.

