Your choice to move to Vanguard (and I'd say the same if you were considering Fidelity or Schwab) is good. If you call Vanguard,
they will help walk you through everything needed to transfer from EJ. Vanguard gets a lot of practice doing this, and you don't have to say anything to EJ.
Advisors salespeople at EJ (and similar firms) have a vested interest in making investment seem complicated. It does not need to be. For example, you could take all your investments at EJ and put them into the same fund,
Vanguard LifeStrategy Growth Fund (VASGX), in each of your Roth IRA, traditional IRA, and taxable accounts (maybe DAF too but I don't know how Vanguard does its DAFs).
One fund for each account. Done. Get on with your life.
Now, there are ways to tweak that plan that could be marginally better, but even that would almost certainly be a huge improvement over what you have at EJ.
If someone messes up a
Backdoor Roth process, it's usually by doing something incorrect with Form 8606. You could use the 'Form8606' tab in the
case study spreadsheet, and compare its results with what you filed. If they match, all is probably well. Switching back to a regular Roth contribution takes no paperwork with the IRS at all: just do it.
One
caveat: when you wrote "simple IRAs" did you mean
SIMPLE IRA (directly associated with a business) or a
Traditional IRA that you each established completely unrelated to a business? In either case, did you include the 31-Dec-2018 balance for those IRAs on line 6 of Form 8606?
There is plenty more "getting started" material available, and sites such as this and
Bogleheads (both wiki and forum) with people willing to help.
A good first step for you would be to call Vanguard and ask them about moving your accounts from EJ. See how that goes, and come back here and/or Bogleheads as needed with questions. Or if you have more questions now, just ask. And good luck!