Ill play advocate
nitrate shows a nitrogen cycle is in place
for sixteen years we find api misread after misread after misread on ammonia. seen some red sea ones too. don't see many salifert ones, S ammonia is great and reliable.
persistent ammonia in the presence of nitrate, any amnt, is interesting when bottled bacteria have not been added.
I think your test is picking up total ammonia not the bad kind, you initiated a skip cycle and really haven't broken rules as long as you didn't introduce new fish without quarantine. cutting it close lol, but I can see you didn't move over a filthy sandbed.
we should confirm your ammonia results. if the fish is pushing it truly then ok, but you mentioned the rock already came from that level of bioload so it was a reasonable assertion. can you get some other diff type of ammonia reading on that tank and post
we expect heavy opercular motion, obvious fish stress, and a real tank smell from true .5 says our thread on reading ammonia levels without a test kit.
there's another universal suspicion to rule out when dealing with seemingly persistent ammonia, among systems that are so ammonia hungry the oxidation can be measured by the hour: the fact that they will digest 1 or 2 ppm right now if you injected it into that tank, yet for some reason cannot oxidize the final .25 or the .5 however its interpreted.
cycles don't freeze like that, that which is linear doesn't just suddenly drop off because a test kit read under fluorescent lights said so (just mentioning confounds for the reading)
you should have water clouding at this level. micro benthic creatures, fanworms on the live rock, all closed up tight.
no corals will open in true .5 sustained.
it takes a massive bioload to cause true curious as to verified readings of ammonia
Live rock creates and retains its own detritus via the tenants, and in many reef tanks the flow isn't sufficient to rid it all.
when we lift/position/move we liberate lots of that in a tank move, spiking the reading above normal baselines isn't crazy sounding.
that combined with your fish bioload, and no natural nitrate reduction possible yet, standard nitrate readings show. A giant water change is what I would do, id pay the lfs to truck me over plenty of made up water, just my take. I think you mentioned moving over old water, good call on the bacteria transfer as if for sure brings some. Tank water has millions of nitrifiers in it via association with the floc that constitutes reef water. source and topoff water can be checked for nitrate import as well.