34" is in the "too close" range for me, and I have seen damage first hand with that size tire contacting on a 6x6.
I like aggressive tyres and that generally means bigger diameter.
I understand Jims concerns but for the type of tracks/conditions where I prefer to use my Pinzgauer anything less than a Swamper usually ends with winching or worse still getting snatched out by a "beefed-up" Land Rover/Range Rover hybrid etc!
Since I purchased my Pinzgauer in the mid 80's I've slowly increased the diameter from 32" to 35":
Semperit All Service (factory fitted tyres .. I've had 2 sets, one old, one new) ~32"
255-85X16 BFG's (new) ~33"
9-34X16 Swampers (2 sets - new) ~34"
Simex 35-10.5X16 ET's (new) ~35"
.....and I've never done any damage to the vehicle (from tyre diameter), but most of my off road driving is done SLOWLY and carefully! ....It comes from driving Haflingers in the bush for 35 years.
If you pick your line, then you rarely get the huge thump from the tyre bottoming out on the suspension.
Oh, and which are best IMO:
The Semperits were OK (way too stiff in the sidewall for rocky terrain etc, but OK I guess if you had 1.5 tonne in the back)
BFG's, a great road and sand tyre, but pretty useless in rough, muddy terrain (even when deflated to minimium psi)
Swampers, great off road and OK on road, "if" you remember you are driving on fresh air a lot of the time (there are big gaps between those lugs
)
Simex, an excellent off road tyre but similar to the Swamper on road.