No hanging about here!

well fair enough you have listed all the advantages of a soldermask, except cosmetic so that makes it easier.
ruffling about in her handbag you could end up with any colour nail varnish

cheap and cheerfull you could leave the bare copper untinned and let it oxidise for a few days, then get a standard pencil rubber and clean just your annular rings and pads etc. if you do not add extra flux you will find that the oxidation acts as a sort of mask, then when you have finished populating use your acrylic laquer to spray the whole PCB.

it sounds also a bit like you may be overdoing it with the solder if it has decided to run off down the tracks , try getting in the samllest guage solder you can. also do you have enough heat in your iron tip and are you using lead free?

I should be able to remember what you could use to speed up the oxidation, would hydrogen peroxide on some cotton wool placed in a sealed jar with the board do it? or is it sliced potatoes?

There are some "conformal coatings" that allow you to rework I think electrolube do one but I am not sure.

Are you mounting SMD's? one trick I have used that may help is to tidyup using thin solder braid that can leave tidy pads especially in a very restricted area and due to extreamly small pitches.

Don't know if this is helping so I will stop

Duncan