Vanguard uses a unique structure for it's mutual funds and ETFs, where both are pooled somehow. Admiral shares and ETF shares are somehow classes of the same underlying thing, making them identical.
So only at Vanguard, you can convert Vanguard mutual funds into Vanguard ETFs. You cannot reverse the process, and you can't convert at any other brokerage. It's only Vanguard mutual funds.
Which do you hate more: paying taxes or holding ETFs?
In another thread you mention an IRA, which has no tax impact for sales. Assuming you also have an individual brokerage account, you are going to have to stomache something you don't like from the following menu:
(1) convert Vanguard mutual funds into Vanguard ETFs. No tax impact or fees, but you dislike ETFs.
(2) convert as above, but then sell ETFs at Schwab/Fidelity. You pay taxes on the sale, but you can use the money to buy mutual funds.
(3) sell the Vanguard mutual funds. You pay taxes on the sale. You then transfer the cash, and buy Fidelity/Schwab mutual funds once the cash is available.
When you transfer ETFs, you remain fully invested throughout the transfer. When the ETFs arrive, you can decide when and how much to sell. You can manage the tax impact, selling ETFs to buy mutual funds over time. Given you dislike ETFs, this is the approach I'd suggest since it lets you control the tax impact.