Yes to the Apple Cider Vinegar. I use Bragg's raw ACV. When I remember to use it, I dilute 1 tsp in 8 ounces of water. I add a little raw honey from time to time. I usually do it before bedtime. Papaya enzymes do work well. As does homeopathic acidil. Acidil is made by Boiron and comes in either the little pellets (green tube) or a dissolvable tablet. I've used both the tablets and the pellets and they both work fine.
So far, the heartburn hasn't been too evil. It was horrible with Ds. Papaya enzymes and Acidil helped, but I was literally cured by a single chiropractic adjustment. I went from weeks of being woken up every single night with horrible heartburn to absolutely none after that chiro visit. So, if you are interested in chiropractic I would definitely recommend it.
The thing with Tums is that it uses a very cheap and rather crappy form of Calcium - calcium carbonate (chalk) - to replace the calcium it normally leaches from your bones. The calcium carbonate is typically bioavailable, unless your stomach acid pH is wonky or neutralized, which is the case if you have heartburn and are taking an antacid. If the Tums neutralize your stomach acid then the calcium carbonate can't work as well. Too much calcium carbonate can lead to kidney stones. The idea that it causes placenta calcification does come up now and then. It's also a pregnancy class C.