I'm not sure there's a clear answer to your question one can give on here. A few pointers, though.
One point is VoIP phone numbers have different regulatory rules for porting than landline numbers. See here on DSL Reports
for an old explanation. Note that was in 2005 and the FCC has since changed the rules to include VoIP numbers in "LNP", as I understand it not all of them and slightly different rules than apply to landline #s.
What I'd suggest is first, determine if GV works for numbers local to your telco switch. More exactly, local to the "telco switch" which serves your NXX prefix number (format NPA-NXX-1234). Search for bandwidth.com
and google voice, and you'll get an explanation. Determine your NXX/prefix and telco switch from these two sources, 1
If above looks doable, then see if there's an third party like T-Mobile that is the leapfrog provider you port your number to before porting into GV.
As you found out you can't go from Time Warner to T-Mobile. Can you port to anybody else? Are any of those anybody else entities that GV allows porting in from? The somewhat opaque list of what mobile providers who can port into GV is here