Balance transfer help

I think I might've worked out the best way to do this but I'm not certain. I've looked at loans but the interest rates aren't great and I'm keen on being able to overpay on an ad hoc basis. These are my cards:

MBNA card - £8100 limit - £4186 balance - 0% until June 18.
Barclaycard - £3500 limit - £2000 balance - 0% until March 19.

I have been pre-approved for a Capital One 0% on BT card but I understand that the limits are typically lower than what I need. My other pre-approvals are MBNA cards so they're no good.

I have an offer on the MBNA card for 0% on balance transfers until May 2020, 2.99% fee.

I have an offer on the Barclaycard for 0% on balance transfers until May 2019, 2.9% fee. Obviously I can't fit the full MBNA balance on there!

In an ideal world, I'd like to have the whole lot on one card interest free rather than splitting my repayments but I'd pay an extra fee for that based on my plan. In a basic salary month I put £200 to the cards (split down the middle), but I often manage nearer £400 through bonuses at work and have focused the larger payments on the MBNA card.

What I'm thinking is:
1) Transfer £2000 from the Barclaycard to the MBNA card
2) Transfer £3150 from the MBNA card to the Barclaycard
3) Transfer £3150 from the Barclaycard to the MBNA card
4) Transfer £1036.30 to the Barclaycard - doesn't make sense to transfer this back given the fee.

Can I actually do step 3, i.e. transfer from the same card twice? If not, I could probably pay the £1036.30 within a couple of months, I have a little (£300) in savings and I'm on with selling some things in addition to my salary.

ETA, the interest rates on the existing MBNA card balance will be 18.9% from 20th June.