Should I consolidate my credit card debt to make it easier to handle, even if that means consolidating my zero percent interest debt with it?

Here's my situation:

Total monthly income: $11464 Total monthly expenses: $10294

This leaves $1170/mo available after our "needs expenses" to put toward savings or debt.

Expenses account for 90% of monthly income. We're spending about $1800/mo on the kids daycare (included in total monthly expenses), and that will be reduced to $0/mo when they are in public elementary school in Fall 2028.

Total available cash in checking/saving: $7319 Total current credit card debt: $36226

That debt is divided into these 7 credit cards:

• $945 0% rate until November 2025
• $5544 0% rate until March 2026
• $14912 0% rate until March 2026
• $2760 0% rate until December 2026
• $12065 remaining among 3 other credit cards that are our "actively use" credit cards not used for balance transfers. We pay the full statements off month to month so we pay no interest, but we had some emergency expenses the past couple of months that have meant we can't make pay the full statements anymore.

Retirement consists of:

• 401k I won't touch for a few decades. Only contributing up to my employer match.
• Rollover IRA I won't touch for a few decades. From previous employers' 401k.
• Roth IRA I also don't touch and don't add to because I can't afford to. Has about $3k or so.

Assets:

• Car which we still owe $30555 and make payments of $600/mo, not included in the debt total above
• Mortgage on house with $398k principal left on the $420k 4.125% loan. Zillow estimate is $625k, so we theoretically have $227k equity. We don't want to pay PMI, so we need to maintain at least 20% equity which is $125k. This means that if we did a cash out refinance, we may get up to $102k in cash, but we also can't afford for the monthly payment to increase, and we have a much better interest rate than current rates. In Spring 2029, our 4.125% rate becomes variable. We purchased in 2022 and did a 30 year mortgage with 7 years fixed before it becomes variable. It has been my intention to re-finance when rates are 4.125% or below so that we can lock that in for the remainder of the mortgage and not worry about that anymore.

Where I'm stuck:

• If we switch to exclusively spending money from checking accounts, we won't have enough money to pay the credit card bills.
• If we keep spending on the credit cards, we continue to "live on the float" and budgeting is extremely difficult.
• The complexity of having 3 checking accounts, 4 savings accounts, and 9 credit cards means that I'm spending about 8-10 hours a month simply budgeting and attempting not to incur interest.
• Pretty much every year, we can't finish paying off a balance transfer card or two so we transfer it to a new card with a 0% promotional rate before we incur the wrath of that first card's interest.

Other details:

• Two years ago, we had no credit card debt but didn't have enough income to build up an emergency savings.
• Over the past two years, we had medical emergencies and house emergencies that totally derailed our monthly budget and made it untenable to use our preferred budgeting tool, You Need A Budget (YNAB), as it's designed to spend money you have and no more. And we had no choice but to spend money we didn't have to cover our emergency expenses. Can't figure out how to use YNAB with all this debt. I've watched the videos, read endless subreddit posts, made my own posts, etc. It's simply not a tool that can manage a truckload of debt spread across several cards.
• We both have very good jobs with great work/life balance, and we are both making near the top end of what our skills can garner on the market for our respective fields, so looking for jobs that pay more are not an option right now.
• More affordable houses than where we live now do not exist in our area, and we place an extremely high value on our community, our children's daycare, and the friends we've made here. It would break us to feel like we had to move away to a cheaper area and deal with the stress of moving away from our friends and community, let alone the stress of moving itself.

I'd like to do one of these options - please tell me if I'm wrong here:

1. Home Equity Line of Credit to pay off the debt. Never done this before and not totally sure how it works. The credit union with my mortgage says, "Rates as low as Wall Street Prime + 1/2%"
2. Consolidate debt with a lender recommended by NerdWallet or LendingTree or whatever so I'm not playing whack-a-mole with monthly payments and entering target dates in YNAB where I can't possibly meet the monthly minimum to payoff by the target date. I don't know how I can properly manage this without combining even the 0% cards into this, as having so many different cards and payoff dates is very difficult to manage.
3. Ask our parents if they'd be willing to give us $36226, the total credit card debt amount as a deduction from what we may inherit, if they even have that. We're in our late 30's and they are in their mid-70's. Maybe they'd be willing to help us by giving some inheritance early?

What is the best option for us? Am I missing anything?

Finally - whatever debt payoff plan we begin, it obviously needs to be $1170 or less per month, as that's all we have left over after subtracting monthly expenses from income, so that we may exclusively use our checking accounts going forward and stop using the credit cards entirely.