I do the same thing with my mechanical media, if I'm not just replacing it. Tap water is fine for mechanical media as long as you have separate biomedia (that isn't rinsed in tap).
Glad your fish did well while you were out of town!
What else is in the tank? I'd just go with a species of cories (depending on what else is in the tank, peppered cories may not be the best idea due to their low temp requirements) and a BN pleco - the chain loaches are likely to outcompete/harass the cories as Redshark mentioned.
If there is some waste or food stuck in the filter media, cleaning it will prevent further nitrate buildup, but it won't remove the nitrates already in the tank.
You shouldn't be adding anything to remove the ammonia/ammonium, and nitrites. Adding anything to remove those will prevent the...
I promise you, rinsing out the media will not remove the nitrates already in your water. They're already in your water, which is why you got a reading when you tested the water, not the filter media. Unless you have a dentitrate filter with anaerobic bacteria or a nitrate-reducing filter pad...
I think you could salvage your tank if you wanted to keep the two firemouths, but it would require frequent water changes to keep the water safe while it's cycling. You could also rehome all of your fish and start again. We can help you come up with a new, appropriate stocking plan too.
I'd leave out the gudgeons - they're rather small and are likely to be lost/outcompeted. I might go with something larger than keyholes, too, like chocolate cichlid or severums.
Are you going to use the aquasoil in the 240? That'll be super expensive - you can grow plants just fine with cheap...
LFS employees often don't give accurate advice, and remember they are trying to sell you as much as they can. Rarely do you need the extras they want to sell you.
The problem will be solved by water changes Cleaning the filter media won't reduce nitrates in the tank.
Yeah, the tank isn't big enough for both species. And really, I don't think its big enough for the smaller loaches by themselves either. The tank is only 31" long, which is a little small for the more active loaches over 3".