One thing I did a long time ago, from not having hiding or magery on my TH, was to put together a rune book of the 16 islands that have T-maps, far enough from the major concentrations of maps to be reasonably safe from leftover spawn, but close enough to be useful.
That book allows me to recall away, the way others hide, without crossing server lines in most cases. It gives you a place to pop in and out from most of the maps that might require unloading. For all the other cases of islands, I carry a boat.
If you're doing primarily the higher (level 4-6) maps, you'll always be on an Island. Take a boat, put the first half your loot into the ship's hold, then use the SHIP KEY as your means of getting back from the bank.
If you're doing lower levels (level 1-3), you should be able to fit 2-4 maps' (at level 3) loot on yourself, several times that for the lower level maps. For those, it's safe and economical to ride a Giant Beetle. Take one greater strength potion with you. Get to know the typical weight of a chest for each level* - if it's gonna be close, use the potion to get out, after the map is done. If it's too close, don't dig until you offload, and go back to the spot when empty.
And, yes, you can dig a T-map while mounted. You just can't use hiding skill while mounted.
*Maps have certain set contents by level - a specific amount of gold, gems, scrolls and regs. These will add up to within a range of 1-2 points per pile of regs, so that, for example, all first level map chests have 27 stones of the first 3, 15-18** stone of regs, then the weight of 6 items.
**theoretically 12-18 (4 to 6 stone per pile), but the range is 40-60 per pile, and one would have to have EXACTLY 40 for the pile to weigh 4 stones. So, it's near certain each reg pile will weigh 5-6 stones (41-50 = 5 stone, 51-60 = 6 stones). The highest chests will have 2 "piles" of some regs, that stack as one pile when the chest is generated, for space, as there are only 13 regs, and the number of reg piles is 3*level.
Hmm...
I think I'll do a post on the relative average loot weights now....