I would not put in the water anything while fasting, if I were you, since chances are that without blood tests it can get messy. One really need to n\know what they are doing in order to put electrolytes in the water while fasting.
The bicarbonate water is used against cancer while feeding. You can do it pre-fast and after some re-feeding after fast.
I believe Budwig's protocol includes cottage cheese from raw GOAT milk. Raw organic goat milk is the only one that we can assume healthy. Its role in the protocol is to use its sulfur-containing amino-acids, in order to make the Omega3 from flax more ready to be absorbed. I actually mix it with my joint supplement MSM - it has organic sulfur; arguably simple lemon juice may be at least as good; then you can have green salad with a dressing of Flax seed + Flax oil + lemon/acid orange/lime.
In any case, all other milks beside goat is probably feeding the cancers in people. It is written many places, and it cancer-promoting properties are associated with all the natural an artificial hormones in milk, especially the growth hormone and the estrogen.
If I were you, I would try to find another food to replace homemade yogurt - like homemade almond(+/-COCONUT)yogurt aka Gorilla milk (recipe on Youtube), at least until you resolve your problem with the cyst; I am sure you will like the Gorilla milk even better (you can use the same starter, and it is done far quicker - only you need to have a good blender for the almonds - use raw, presoaked for at least 8 hrs). You can order raw almonds at email@example.com.
I would also crack open and eat any naturally bitter nut or pit I come across - apricot, peach, prunes about 6 pits a day - vitamin B17 in them is an anti-cancer substance. There is a misinformation that you can get poisoned by the CN- (cyanide group in it; .. but hey! even B12 in stores is sold as CYAN-cobalamine aka CN- group in it) - you will never ever get intoxicated with 6 pits a day! When I was kid we ate all afternoon long apricot pits. Maybe this is way my family has no cancer incidence. I can eat 20 pits in one sitting, my body just tells me 'thank you' in the process :)
Animal milk/dairy is the most acidifying food (opposed to alkalizing). You can alkalize not only with bicarbonate -- all the raw food in the world is mostly alkaline - especially the greens, that are best to be juiced for people who need healing, like us. By greens I mean not just romaine or spinach, but the whole spectrum - parsley, cilantro, chard, cresson, cabbage, beat-leaves, carrot-leaves, beyond them carrots and beats make miracles when juiced. I realize that a good juicer for leafy greens is a must if someone is committed to health. If not yet available - eat them by the tons to replace all these carbs - ... sorry to pick in this, but I feel you are kind of fixated on rice. Is it brown rice at least? (or wild, black, red - these are the ones which are not depleted).
If greens are not too available around your area Spirulina and Chlorella (bought organic in powders - for best price for quantity - about 25$ per dry pound is normal, and they have value for every single cent you pay for them, times ten; you put them in juice or water about a tablespoon per drink) do wonders in terms of detox and alkalizing. You can detox every single day just by having them in drinks (not soda and not coffee - these are deadly-acid)!
Concerning your re-feeding ... it is not how easy your system can digest back your old food, but what is best for your healing ... you were too quick to eat that rice, especially combined with yogurt, topped with coffee if all of this was not enough; call me petty, but I believe the right thing would have been to be on raw food at least 2 weeks. The body continues the detox on raw and builds back the best on raw. If you give it depleted rice and hormone-laden yogurt ... it is going to say "that cyst? - I'm gonna keep it, or grow it back because I need to dump the garbage somewhere". It could have very well been that it still shrank during your fast, only to expand back. It is still not late to go back on raw and aim now for 60-70% raw food and above, organic if possible when possible.
At True North you will have doctor's supervision and lab tests, so you can fast longer. It may be reasonable to get there around day 15 or day 20 of your fast, if you can organize smooth travel while fasting (not to faint on the road ...) if not maybe get there a little earlier.
I wish you setting the right plan.