Conker, the lower pockets will be too big for the sleeves. What I've seen (my buddy has a beauty RAID jacket in woodland ripstop), is the bottom pockets moved to the chest and the top pockets on the sleeves.
You might try to position the large pockets on the chest in a manner similar to the Crye R6 jacket. Remove the pocket, and with some extra material sew a back panel to it before you replace it on the jacket. Then secure the pocket to the jacket with sitiching on the top (careful not to sew the thing shut; just stich along your new back panel), bottom, and center edges. Leave the outer side unstitched, and you have a slash pocket accessible through the arm hole in your armour.
It will also be easier to put back on the jacket than a backless pocket, since with your new back panel it will retain its structure and 'footprint' while you're messing with the sewing machine.
The other option is one of the old woodland aircrew jackets, popular for their FR capabilities. Maybe eBay? Or just go for a Tru-Spec ACU jacket in woodland. Plenty of guys go that route, but I think they're useless.