You've left out a vital bit of strategy regarding the Gnome King levels which occur every five (5) waves.
During the first couple of Gnome King encounters it doesn't matter much how you fight him, however if you are playing Solo or at anytime at the Rainbow level (Wave 25) and onward you need to pay strict attention to when the King summons reinforcements.
There will typically be two calls for reinforcements- one of Gnomes and the other of your Nemesis. When battling at the higher waves it is vital that you break off from the Gnome King and clear out each spawn of reinforcements before going back to directly combat the King again. If you do not clear these reinforcements out, especially when battling multiple Gnome Kings you will have a situation where you can easily be overwhelmed by their numbers.
When you break off combat with the Gnome King he will follow you for a bit but he may decide to Destabilize Time. If the King is destabilizing time while you're clearing out the reinforcements he called then you'll want to shoot him just enough to move him to come after you. Alternatively you can continuously blast him just a bit here or there while you vanquish the reinforcements so that he won't go off to try to Destabilize in the first place.
Do this break off/clear out/re-engage on the Gnome King levels and you have a much better chance of making it into the higher Waves whether you're playing solo or as part of a co-op.
