Firstly we only saw one Aschen colony world. They would have industrial bases on other worlds.First we never see any indication of a major industrial base on the Aschen colony world that SG-1 visited. It is entirely possible that their homeworld held all their industry and supported a truly massive population. This is why they tried to depopulate their allies and then turn them to agriculture. They might be complete hypocrite assholes who talked of population control while demonstrating none themself.
This would suggest that while some Aschen and their large harvester ships may survive the loss of their homeworld to the Blackhole none of their industrial base would exist. So a few Aschen with hightech farm implements might be all that is left of their society.
Second, everything about the Aschen has demonstrated subversion and manipulation of lesser tech planets for their own benefit. This would mean that their weapons tech no reason to be very advanced. Instead their advances have been in areas they have focused on which is biological and genetic warfare.
Secondly, several of the Aschen colony worlds have Stargates. They could have dialed the co-ordinates Earth gave them through one of their colony worlds. This would led to the destruction of the colony world but it would keep their home world safe.
Thirdly, the Aschen technology we have seen is very advanced and could easily be applied for military purposes. The Aschen must have some kind of military, if for no other reason than to keep order on their home world. Even countries like Switzerland keep a standing army and the Aschen have more reason to maintain a military than Switzerland.