Why timers?
Just let the last response of the previous /whois command trigger the next. Its then impossible the server sendqueue overflows.
Regarding the server receivequeue, if the sendqueue never overflows, then the receivequeue doesnt either, and /whois nick1,nick2 etc doesnt suffer this problem at all, since the server sends a RAW 416 too many lines in your output, which just stops the responses after that amount, so a part of the passed nicks need to be re-whoissed.