Heat molding almost completely undoes punches, because it lets the leather relax back to an earlier shape (one that was probably impressed into the leather when the boot was made, by carefully heat molding at a higher temperature, under very high pressure, maybe with steam, by experts). So I agree, punch
after heat.
And punches can only make minor changes, unless you keep redoing the punch.
I eventually bought a cheaper version of a punch for myself - variously called "ball and ring pliers", "hoke and ball pliers", or the iron or steel variety of bunion stretchers, so I could keep redoing it, every few weeks. I have a few tips on that at
http://mgrunes.com/boots/boots.html Basically, you want to use a hand-held hair dryer to warm up the place you are going to stretch (basically, a local heat mold, under pressure), then tighten the ball and ring done on the place (and maybe put a thin piece of cloth on the outside portion, if you care about keeping the surface nice), come back in an hour, re-heat and re-tighten, repeat several times, leave it overnight, re-heat and retighten, and give it at least a few more hours. You can also first soften the leather with alcohol, though that won't help with the stiffening elements that are between the layers of leather, and it isn't all that good for the leather. You probably don't want to apply alcohol to the outside, because it would tend to remove the finish and gloss layers. To some extent that iterative procedure is needed because a ball and ring pliers can't generate as much pressure as the industrial strength punches that the pro shop probably uses.
And yes, nylon laces are still available. So are waxed cotton laces, which slip back less easily than unwaxed cotton. I use round nylon parachute cord or utility cord, because it is very easy on the fingers, and is easy to tighten. I chose a diameter which grabs the lace holes a bit, so they don't slip back much. But people here have different preferences from each other. There are a number of different ways to lace your boots too.
This whole learning process of making skates fit and work for you can be an interesting journey. Try to enjoy it, rather than be annoyed by it. When you are done, you just might be able to make your other shoes more comfortable on YOU than even most podiatrists can manage.