Question: I want to avoid my program being simple to have the license-verifier part removed from.

I don't want to use a commercial obfuscator because:

1. Of the cost. And though they can do a better job than I – they
too don't make it impossible to crack, just harder.
2. It seems that sometimes obfuscators cause bugs in the generated
code.

Obviously, I will be keeping an un-obfuscated copy for maintenance.

Answer: 
I once had to hide a license verifier in code that the customer could modify. Conceivably, they could have removed it if they knew where to look. Here are some tricks that I used at the time.

1. Give your verifier classes, assembly names, and variable names that look like they actually do something else.
2. Call the verifier from multiple parts of the code.
3. Add a randomizer to the call for verification so that sometimes it runs, and sometimes it doesn't. This will make it harder to know where the verification code is actually coming from.

I should add that all of this is defeatable and could cause serious maintenance headaches, but in my particular scenario it worked.
I have some suggestions that you may find usefull. 

First of course you can use free obfuscators like the one that comes with VisualStudio. It's better than nothing. 

Second you can write your license verification code and once it's working fine, refactor it as much as you can, change class names, member variables, local variables and methods to something like c1, v1, l1, m1 and so on. That's basically what obfuscators do.

Third, do all of the above.

Fourth, write your licence verification in unmanaged code (C++, Delphi) and make it a DLL named something important like core.dll, net.dll etc. You can also put some decoy methods in there that would do nothing important. Make many calls to that DLL from multiple places of your code and pretend that you do something with the results of those calls.