I have written three articles on cycling for another site. The first was how to do a fail safe fishless cycle in 5-6 weeks. The other two were how to rescue a fish-in cycle gone wild. I was supposed to write a 4th article on using plants or seeding bacteria either with a proven bottled product or items from cycled tanks.
I am having a hard time understanding your approach. For one, cycling is the direct result of adding ammonia. You cannot cycle only the sump unless you compensate for the other 100+ gallons in the main tank. How much water will depend on the decor. But then there will be another 25 gallons in the sump. Tanks hold 10 -20% less than the advertised volume depending on what is in them and then because they are never filled 100%. So in your case we are looking at between about 130 and 140 total gallons. But you are using only 25 for your cycle. That is 20-25% of the total ultimate gallons in the system.
So if you want to follow my basic article, it calls for dosing to 3 ppm. But you will need to cycle the sump to handle 4-5 times that or 12 -15 ppm. Considering that ammonia, using an API text kit, at about 6.5 ppm will stall a cycle, you need to be a lot more experience to do this. I do this sort of thing when I run my bio-farm for cycling filters. It requires that you build up the bacteria oer time so there are enough that a high concentration can be processed rapidly.
You should be using a dechlor that only detoxifies chlorine but not ammonia. Sodium thiosulfate- the cheapest smallest i could find fast was here for $10
https://www.amazon.com/Sodium-Thios...den&sprefix=sodium+thio,lawngarden,224&sr=1-8
Next, the easiest ammonia source would be ammonium chloride ( what i use). Again small amounts are not so easy. Dr. Hovanec sells it as well as his One and Only nitrifying bacteria. This is the only bottle bacteria I will use. Tetra Safe Start Plus is very similar.
The above can get you cycled using my directions. But you still have the problem of trying to complete a cyle for 130 -140 gallons of water using only 25 gallons. I can do it, you likely cannot.
I prefer not to use things from other peoples tanks to jump start a cycle in my tank. But I have 20+ tanks and can do that sort of things completely in-house.
I am not sure how you are getting oxygen into the water in the sump. Nitrification in tanks is an aerobic process and oxygen is important.
I would not use any bio-balls. Years back i had planned to use a 40 long tank and Poret foam on a sump for a 125. I worked with Dr. Tanner of Swiss Tropicals to design the sump. It basically used 4 sheets of Poret foam 3 inch thick with about 1 -2 inches of space between them. The first was 10 ppi the nexy 2 were 20 ppi and the fourth was 30 ppi (or it could be another 20 ppi). The higher the ppi the faster the foam will need cleaning.
I also discussed the best way to use Poret foam in a canister. He said use 100% poret and nothing else. I did this in one of my Eheim 2026 Pro II. Mot blu or white floss pads, just 20 ppi Poret. I ashed Dr. T when I should clean the Poret. I told him my other canisters were cleaned every 6 months. he said clean it when the return flow slowed so I could notice it. That took about 3 years.
Back you your cycling problem. My best guess without a bit more info is there were several problems. First there may not have been enough oxygen. Second, the low dose of ammonia may have mostly evaporated before many bacteria could establish. Since you did nothing to seed bacteria then you started with very few.
I think you have to go back to square one. The foam bubbles are not a good thing. It may have to do with something in the ammonia. I think the sump needs to be cleans as does the Poret and then you begin anew with the sort of products I suggested. You can buy a big jug of dry ammonium chloride from Jehmco
AMMONIUM CHLORIDE:
Pure ammonia for “Fishless Tank Cycling” method of setting up new aquariums. 1 tsp will provide approximately 4 ppm ammonia in 100 gallons of tank water -
https://www.jehmco.com/html/water_conditioners.html scroll way down it is near the bottom of the page.
If you want to get the Dr. Tim's bacteria- get it on Amazon.
https://www.amazon.com/DrTims-Aquat...nly+Nitrifying+Bacteria&qid=1619672444&sr=8-8
This will cycle up to 120 gals. But it costs $31.77. You can use a smaller amount and then spend extra weeks getting the bacteria to reproduce enough to reach the needed level.
With the Dr. Tim's you should be able to cycle your tank in 7-10 days for close to a full fish load. But I still urge you to cycle the sump and tank with the full amount of water and not just the sump. It will make things much easier. Doing it all in the sump requires testing several times a day and adding ammonia (as ammonium chloride) twice a day as well.
If you want to do what I have suggested, I can PM you a link to the cycling article which walks one through the cycle from day one to completion. It requires about 6 to 7 ammonia additions and the timing is based on your actual test results for ammonia and nitrite. The article is on another fish site and i do not want to be accused of promoting the competition. I have not been active on that site for years but they still have my articles there.