Things that will decide whether the narrow width is gonna be a problem -
terrain(smooth/level = good, rough/sloped = BAD)
caster size - you got that covered, unless you're on sloped/gravel (or worse)
Center of gravity - lower is better; which is why, if you're gonna mount the vise on the long side, you might wanna consider Truck Diagnostics' post # 62, this thread, and ONLY move the table with vise hanging LOWER - either that, or reserve a place on your LOWER SHELF for the vise, and ONLY move table with the vise down lower - (less of a PITA than a tip-over

)
Where you push/pull on the table to move it - the
LOWER the force is applied, the less likelihood you will tip it (might wanna consider something like a "wagon tongue" handle that attaches just above the casters, and push/pull with THAT) - in the same vein,
push/pull LENGTH-WISE will be TWICE as stable as moving the table SIDEWAYS.
Example - I can tip my 3'x7', 1" thick table (approx. 900#) over BY HAND pushing sideways (not easy, but doable) - but NO way can I do that LENGTHWISE...
These are considerations I would look at if building a portable weld table; but YOUR level of OCD is probably lower than mine

- ... Steve