Bank tabs, all my guys and gals have Frozenweave bags for the bank, and I got rid of all of the BC and earlier stuff to two bank alts with full Frostweave bags.

I have 5 bank tabs too, one day I'll get the 6th.

Do as much combining as you can - if you're saving ore for JC and Blacksmithing or Engineering, keep half ore, smelt the other half, bars take up less space. Same for herbs - if it's primarily for an Inscriptionist, mill half of them, the pigments take up less space. Same for leather - if you know you need mostly heavy leather, combine the half of the Borean, and combine all the scraps.

My biggest issue was meat, for cooking, it took over a bank tab for a while. Your post reminded me I need to make bags for another alt for meat.

The biggest issue I've had is gems, as cut gems don't stack, so I leave those alone and only cut when I need, or I'll cut a stack of green gems, and keep the perfects.

If you can afford a 5k bank tab, drop a few k on Frostweave bags for everyone, and make a couple bank alts and kit them out, and use those slots.