Typically I use the forged Speed pro 6 pack piston # 2244 Maybe , unless I build a stroker which is generally the case when building a 440 anyway .
I don't use cast or hyper pistons ever
360 are cheap easy to stroke to 408 , W2 heads make a lot of power , you have the heads so that is what I would do ,
SS springs & double adjustable shocks should hook it up . Make sure everything is reinforced & Square in the rear suspension , mine had ladderbars , would carry the front tires...
Correct the front brg can be 307 or 308 , the front brg retainer is 4.35 OD with 307 , 4.80 with 308 , or 5.125 with 308 & OD you will need a different bell housing or an adapter ring to use the 4.35 with the 4.80 belhousing , but they all still bolt up , I used to machine the 5.125 retainer...
Lifters have been a problem for years many poor quality ones out there , Johnson are the best brand , you can easily swap them out without removing the heads or intake using a good magnet , I would try that before sending the car away to be worked on , the poor quality lifters can stop holding...
Are you getting power to the heater motor or the switch at the dash , possibly a blown fuse , you need to start tracing the circuit .
I asume the hoses are connected & the heater valve is working to provide water flow .