There is so little size difference between what passes for a group 29 and a 31 that to recommend one over the other is simply ridiculous.
We're are talking a difference of 4mm in length and 2mm in width if this site is to be believed:
http://www.evdl.org/pages/bcigroup.html
Heck batteries called the same group size among different manufacturers can vary more than this depending on handle design.
And for a single battery needed to support a huge amp load for a short time, I do not think telly com AGM batteries are the right choice.
I am not saying a large bank of them are not good house batteries, only that a single tellycom battery is likely not the best battery to support the occassional huge inverter load.
The Op has expressed a desire for only one battery. I think A group31 Northstar or Odyssey AGM could likely support a huge inverter load for the longest period before the low voltage alarm on the inverter screams for mercy.
Also they can accept huge recharging amps without worry.
I do not know, but niners huge tellycom 150A acid rich or acid starved telly battery seemed to hit absorption voltage with less than 30 amps.
I can hit my well depleted 90Ah Northstar group 27 AGM that has 400+ deep cycles on it with 65 amps for nearly a half hour before voltage hits 14.7v and amps begin tapering.