Get the Tstat and gasket from the dealer, it has the correct bypass hole. Install the tstat with the little hole at the 12 O'clock position. Same with the pressure cap, OEM dealer and if you really want to save yourself some trouble down the road do the hoses also. Again, dealer supplied, the new OEM heater hoses will have the clamps already on them and the lower rad hose will have the anti-collapsing spring in it as well as the hose protectors around the outside. They also fit and are not 'generic', have the correct sized ends and bends.
When removing the heater hoses don't pull or wiggle them off, instead slit them with an exacto knife or other razor knife length wise then peel them off gently. Break one of those heater core bungs off and you just added a couple of hundred dollars and 8 hours of labor to the job.
Just a thought and I'm going to try this myself the next time I drain my system in the driveway and don't have access to the machine. Hook up a wet/dry vacum cleaner [strong one] to the top radiator hose disconnected from the radiator, plug the radiator top bung and turn the shop vac on, this is after you have done the initial drain of the system unless you have a big tank I'm thinking
. After using the air run snap-on coolant flush machine this may do the same thing and evacuate more coolant. Remember also to turn on your heater so that coolant can be removed from that too. What I don't know is if a shop vac can generate enough vacumn to do what the snap-on machine does with shop air, it might work but dunno know for sure. I do know that it will take longer if it does.
Remove the overflow bottle, drain it and clean it out, put it back in and refill with new mix to between the hot and cold mark.
When it comes time for refilling have two gallons of mopar coolant and two gallons of distilled water. Initial fill just dump in the first gallon of pure coolant and one gallon of distilled water, thats a 50/50 mix, then dump half the other gallon of distilled water into the empty coolant jug, top off with pure coolant and add the remaing half gallon of distilled water to the half filled pure coolant bottle, that gives you two 50/50 mixed gallons in the correctly labled jugs.
Now comes burping the system, take about 30-45 minutes, nose up a bit.
Start her up, top off with coolant and let it bleed air out, you can see the air in the top filler hole of the rad if you keep it full to the neck, it will look like fuzzy green soda, just let it run and keep it topped off till there is no more fizzies. Once you are convinced that all the air is out, engine running, race the engine, coolant level in the neck drops, quickly top off, pop cap on and the system should finish bleeding itself from there over the couple of days.
Before I did any of this I would drain the system, add a bottle of prestone 7 hour flush and refill with water then drive it, with the heater on. Might as well get as much gunk out of the old system as possible especially the stuff in the block and heater core. Then backflush it with the prestone kit. Then do the cooling system stuff you had planned.