My HELOC has now grown to approximately double my mortgage
So, how did it get there?
If it was a one-time thing like you had major medical bills from an emergency, did a major renovation on the house, or maybe had to pay to ransom a loved one... go ahead and refinance this week. (Assuming you don't foresee it will happen again)
If you aren't sure how you got to this point, and you don't change something, refinancing is a poor choice because you'll be worse off in two years (worse off because you are out-spending that "substantial" income).
Now, to answer the question you asked:
What would be the best way to consolidate these two debts?
But, I think the question you want answered is:
"How do I minimize the interest I'm paying?"
Consolidation may not be the best move, because interest rates have gone up. If you've had your original loan a while (and I hope so) it may be lower than the current rates.
A quick trip to BankRate shows current refinance rates are about 4.6% for both 20 and 30 year fixed rate mortgages (assuming a 715 credit score and 50% equity).
Home equity loan rates are about 9.5% - and I'd advise a loan not a line of credit (LOC) because you've already rung up double your balance with a LOC - since you have a good income, have the discipline to just live off it.
If you do refinance be sure that you continue to pay what you're currently paying with the higher interest rate instead of the minimum payments - you'll pay it off much faster.
You didn't give us any actual amounts nor did you provide either of the interest rates, so that's as far as I can go with it.
A reason that your payments would be only slightly higher with both amounts as your current payment is that the life of the loan is longer.
Use the same mortgage calc to add up the total interest paid if you continue your current loan vs. the total interest paid plus refinance charges ($500 for appraisal + lender fees + etc.) to get the new loan.
Compare those amounts and I expect you'll see something different than what the monthly payment amount is telling you.