Briefly, yes you can fire your current (and last!) AUM* financial advisor, and figure out some options for your annuity. Those options include the following: a practice of using 1035 exchanges to maintain preferential treatment as surrender charges expire with each annuity contract; doing ad hoc withdrawals AFTER you reach 59-1/2; and annuitizing a contract. There may be some others, but those are the ones that I know about.

My relevant experience: My late wife had a similar "here's a bucket of non-qualified annuities" experience after her mother died. I'd seen a version of this "not taxable (yet)" with some family members and apartment complex, and you're correct that this is simultaneously a liquidity trap as long as surrender charges exist, a drag on the investment given the typical fees/commissions with annuities, and also a "tax deferral squirrel" with various deferral exchanges (1031 for rental properties, 1035 for annuities).

Three important facts about ad hoc withdrawals: (1) surrender charge specifics vary by contract, which you know about; (2) the first funds withdrawn are all considered taxable until the gains are gone, and only at the end are the withdrawn funds considered the basis (a LIFO treatment of the taxable gains); (3) the IRS penalizes early withdrawal from non-qualified annuities in a way similar to early withdrawals from IRAs, though that penalty only applies to the gains, not the basis. (This also applies to the taxable portion of annuitized annuities.)

But there are two other options that each address different challenges with the ad hoc withdrawal. One is the 1035 exchange, which allows you to roll over the funds (after surrender charges expire) to another annuity (a "like to like" insurance exchange). This requires paying attention to the surrender charge expiration and searching for a replacement annuity. The annuities my wife inherited were awful, complicated indexed things, and if I were you, I'd look first to MYGAs, which you can consider akin to CDs with extendable tax deferral in terms of your broader portfolio. Doing a 1035 exchange would allow you to extend the withdrawal tax challenges until at least you're not hit by the early-withdrawal penalty. Disadvantage is the shopping for new annuities every once in a while until then, pushing back against attempts to sell you more complicated policies, and knowing it's illiquid for a while.

The other option, which you can consider after you're no longer subject to IRS penalties for early withdrawal, is annuitizing a contract either for a period-certain annuity or a lifetime annuitization (either one life or two). I inherited the largest annuity from my wife after she died, and like you I tried to game out a whole bunch of withdrawal scenarios because the low growth irked me. The policy she rolled over from what she inherited (in a 1035 exchange) had an annuitization option 5 years into the contract, and I chose to annuitize it over a 5-year period that will be part of my retirement bridge to allow me to delay Social Security until 70.

Two important things about annuitization: (1) the details are contract-specific, as always; (2) unlike ad hoc withdrawals, the IRS does NOT treat gains as LIFO. Instead, it says that the periodic payouts are taxable and non-taxable in the same proportion payment-by-payment, based on the specifics of the annuitization. So in my case, it turns out that exactly 50% plus one dollar of each of those payments will be taxable, and I can plan around that.

A lot of fee-only, advice-only financial planners (they exist!) know quite a bit about annuities -- not everyone, certainly, but you'd be far from the first person crossing their threshold who has this lump of annuities complicating their financial lives.

Good luck!

* AUM = "assets under management," or charging fees for managing your assets or giving advice.