Costs? You've yet to fill an auto tank with fuel for a week of driving with those "costs." IMHO You've not added up any
costs as of yet.
Go out to the pub for fish & chips plus beers one fewer time this week and you are square.
I would have made a deal with the shopie chap you bought the FW from to throw in the removal of the old fixed cog plus a dab of grease to spin on the new FW. Seems like you'll only ever use the new tool to remove the broken fixed cog once and never need it again -unless you intend to get more seriously into wrenching on other bikes. Plus you don't really need a tool to remove a fixed gear cog if there isn't a lockring -just
ROTOFIX the damn thing off. Often one can just tap off the old lockring with a hammer and an old sacrificial screwdriver if it hasn't been locktighted on (you'll probably ruin the lockring but who cares?) -but I hesitate to even mention that given your past history...