I don't see a schematic in your post.
So, you're after a nixie tube power supply? I believe there's plenty of examples floating about on the web and in this forum.
I am unsure of what your problem is. You say you have a small transformer.. that has 110v out.. from what? mains? or a primary switching circuit? If the transformer is on a board built as a DC-DC converter then a voltage multiplier won't help, but it should taken straight off the transformer. You are correct in assuming the output with 'sag' with current draw, but how much, depends on your setup.
Are you worried that you'll 'blow' a nixie tube if one of them fails causing the power supplies voltage to increase? If you limit the power supply voltage, it won't. Adding a permanent load should indeed keep the voltage lower if its coming from a voltage multiplier.
I think you would get more answers if you stated the problem more specifically.