MXMoni shouldn't affect you hosting a room. Unless you are using the built in hosting features of WinMX I suppose it could cause some kind of issue there. In any event I'd recommend using a dedicated hosting client such as WCS, EServ, Ouka, FXServer or ZCS. WCS and EServ have Linux native builds while Ouka, and FXServe would require Wine and ZCS would require you to use Wine & Mono.
I've had the issue you describe where WinMX crashes randomly but MXMoni stays open. This is however I believe unrelated to MXMoni as I've had this happen when MXMoni is not even open. On both Secondary and Primary.
I have no experience iwth Leechhammer on Linux under Wine.