The best way to do this is to avoid banking at the alter. I have the Lunar spell book equipped and cast the Ourania Teleport spell to get near the alter. After making the runes I just cast the Moonclan Teleport and use the bank there.

The advantage is that Moonclan has a summoning restore point on the way to the bank and you only have to run to the alter, not back. Also don't have to pay 20 runes to bank which is even more expensive when you use 4 pouches.

I'm definitely not much of a runecrafter, but I was doing some runecrafting at the ZMI altar the other night, and realised it saved me some time to just teleport straight back to Ourania instead of to Moonclan first.
According to the RS Wiki, "Moonclan Teleport costs 627 coins for each cast". Say you need to access the bank 3 times per trip (filling pouches and follower), the runes you pay cost less than a teleport to Moonclan does. You'd just bring yourself a stock of several thousand mind or fire runes and be good to go for a while. As these cost 9gp each, you'd be spending 540gp for each run. When you need to recharge summoning, use the Moonclan teleport instead.

Or does this not work because you have 4 pouches?

Anyway, good luck. I think you'll make it.

One hassle with banking at ZMI is the tendency of your summoning creature to close windows when something major happens even if you aren't done yet. If I manage to get to the bank and get my bank window open before my Terrorbird re-appears, when it does appear it shuts down the window as if to say "I'm here". The same thing happens when there is only 1 minute or 30 seconds left before the creature disappears. I've noticed this with Bull Ants as well. Its irritating behavior when it doesn't cost anything to bank let along after I just payed out 20 perfectly good runes.

Hope you can make it, it's a very hard thing to achieve =)