Water changes won't damage your biofilter so long as you remember to treat for chlorine/chloramines. Change large quantities (like 50%) twice daily and you'll have better luck getting your levels down. Small changes mean smaller dilution.
For example:
If you change 25% of your water and have say 10ppm NH3, you now have 7.5ppm NH3, so next time you change (assuming there's been neither any input nor bacterial breakdown) you have 5.6ppm. But of course, you know that there is both production and consumption going on.
If we do the same thing with 50% changes, after the first change you're down to 5ppm and after the second 2.5ppm.
Do 2 50% changes back to back. Remove 50%, fill, remove fill. This will be a 75% water change and should get your ammonia levels down to a "safe" level or at least sub 1ppm.
There's really no such thing as "matured" water, you want your tank water to be as close to source as possible. I say source because although this normally means tap water, some folks choose RO water or boost alkalinity for african cichlid tanks. I think that it will take a very long time to dispell the myth that seems to be pervasive in this hobby that old water is good. I frankly can't understand how it came to be, but there it is. In the wild fish live in regions of almost constant water turnover, with few exceptions. Even lakes generally have a high turnover rate compared to most aquariums, and yet there's this belief that old water in which your fish have been living (and carrying out the processes of life, nudge nudge) is better for them.
Stability comes from new water, not old, and what fish need is stability.
I don't mean to flame you harmony, that rant wasn't directed at you, it's just that your post is about the fifth in two days (both on this forum and on the local one) where people have argued with me about keeping old water and not changing too much water.
As long as you have some surplus of NH3, your colonies will continue to grow. Keep pH and temperature steady and keep your NH3 levels sub 1ppm and your tank will cycle and your fish will not be harmed too badly.