If i understand correctly the 2-way game loads your 2way map trough your mala plugin. At that point UltraMap uses your 2 way map.
On the backside of things, MAME loads the default MAMA 2way analog map. If your 2way U360 map in UltraMap is not setup correctly, it's impossible with your setup to use anything other then the range that the map allows. For example, after u load a 4way map it's impossible to use left/up, right/up, left/down en right/down because corner's are not allowed.
When the game is loaded in MAME use a keyboard to 'alt-tab' out of mame an load UltraMap (run as administrator) and check which movements you can make with your sticks. If you can only move left and right, you won't be able to set up and down.
A simple fix could be to replace your UltraMap 2way map with your 4way/8way map. New versions of MAME use a analoge map them selfs, so mapping trough UltraMap is not really needed anymore.
You could also take a look at this:
http://www.headsoft.com.au/index.php?category=mame&page=joymapYou could use this to make special maps for mame. If it's just a single rom that gives the problem, create a map for that particular game.
If you need a fix for all 2way games, make a working map and replace the default MAME map.
Don't know how big your space issue is under your CP but i would always try to remount the sticks the correct way. The top mounting plate can be mounted "landscape" or "portrait".
Sorry for the long story, hope this helps.