OK- here is how to do this. You need not to do a fish in cycle, At best the fish wont die and at worst it will.
Using a cycled tank is not a requirement ti keep fish, but it makes it safer and is a whole less lot work. So what does this mean here? You can park your betta while you cyle its tank if you want. Here is how to do this.
You do not need a tank, you just need a safe container. A Rubbermaid costainer that holds a few gallons will be fine. You will need a heater and an air pump and air stone. You will set this up like a tank but you will not need a cycle. Instead you will change the water every day or two. That will be determined by what size container you use and by testing for ammonia. The bigger the container the better in this regard, to a point. 5 gal. would be fine.
Test after 24 hours. If ammonia is .25 ppm or less, you can go another day. Do not feed the fish daily, in fact every 3rd day is fine. Healthy fish which are not very young can do fine without food for some time. The smaller the contain you get to "park' the betta, the more frequently you will need to change water. You and these water changes are the filter for an uncycled tank for the duration.
You need to vacuum any waste from the container at least once a day- remove fish poop and any uneaten food after you feed. If you can put in a fake plant or two so the fish can hide, this will help but if not it isn't a huge deal. A couple of live floating plants would help but are not a must. The water changes will keep the fish safe, the heater and air will keep the water warm and clean. It is very important to do the water changes, without them you will be back where you are now.
Next, the nitrifying bacteria are live and they reproduce by dividing. They do not form spores. Stability is a bottle of spores. As a rule the last option for a tank is to add some chemical/cure when it isn't really needed and wont help. It may hurt. You did right getting the Tetra SafeStart, the problem is the surgery in the middle made what you were doing difficult to succeed. When we add live bacteria to a tank, it needs ammonia. When this is a bottled product like Safe Start, it takes the bacteria day or so to wake up and to go to work (they are dormant in the bottle). One of the first things they do is to attach to hard surfaces and create a bio-film in which they and other bacteria live and work in concert.
You needed to be actively helping the bacteria when you had to stop for surgery. So what happened to them is hard to say. But a ton of them should have removed all ammonia from 1 ppm pretty fast, 2 days max. After than they needed to be fed ammonia. Normally established bacteria go dormant when what they need is suddenly gone. But it takes a while for them to settle in and ammonia additions are needed every few days or sooner. Since you could not do them..........
If money is a problem that makes your options more limited. To add the proper bacteria or to get live plants costs money. If you have more of the tetra product unused this would help here. It would make it possible to do this all very differently. the same applies if you can get a bunch of live plants. But I get the impression that you may not be able to spend much more at this time.
The above solution using a container to park the fish will give you time to insure its permanent home is well cycled before the goes back into the tank.
As noted above the cycle will slow the lower the pH. At 8.0 it appears to stop. It does not, it just works way slower and it takes longer to oestablish the cycle. There are few cheap options for changing ones water parameters the bigger the tank involved is.
I have tons of excess live plants and am happy to mail you some at no cost to you, But They likely would npt get there for some number of days as the USPO is not as fast as it used to be. I have anubias, java fern and long leaf hygrophila. This last one is a fast growing stem plant you can float. I can afford to cover the shipping cost for few plants as well, so do not worry about that part. I could send some crypts but they need to be growing in substrate.
If you want the plants I will need a name and shipping addy. I would send them Priority mail in a fixed price box. I am in NY not far outside NYC. Unless the temps are really high they should be fine. It doesn't make sense to send them in an insulated box as it would be cheaper to send money for you to buy them locally.