You are asking about how to hybridise different threaded models, but I would not give up on AF just yet as it can do complexes.
AlphaFold2 is conceptually amazing, but does have some issues to such an extent that I blogged about common problems I was getting so many questions. Specifically, it models one protein chain in isolation.
In the RoseTTAFold paper David Baker and co. mimicked the AlphaFold2 algorithm hinted at from the CASP14 competition. They discovered that if multiple chains were given as a protein concatenation, with suitably long polyglycine linkers, a good oligomer or hetero complex could be resolved. Quickly after the public release of the Colabs notebooks of AlphaFold2 in the Twittersphere there were reports of homo/hetero-oligomers being resolved nicely. Of particular interest is the report that if you put a spurious pairing you get bad results —i.e. a control of sorts.
This strategy many be applicable to your homohexamer.
Your long random loop could be binding something else, so if you know what you may also then want to try with that something else!
Threading, ab initio and hybridisation
Given a template PDB and an aligned sequence a threaded model of the sequence can be made by replacing the residues where required. SwissModel, ModBase and Rosetta partial_thread app does this in the open, while Phyre2 and I-Tasser do it hidden in the pipeline.
If a span is absent, SwissModel and others will try to predict from scratch (ab initio) the span.
Features of different threaded models can be stuck together (hybridised) manually or automatically as do Phyre2 and I-Tasser. The RosettaCM (comparative modelling) toolkit is really handy in that one can customise how different parts are treated by adding Rosetta constraints (restraints in crystallography parlance), ligands etc etc. It should be noted that threaded models are faithful to the template, so can be converted into the same complexes as the template, but as soon as they get hybridised they loose this.
You currently have various threaded models against a panel of homologues of your choosing and are looking to hybridise them based on your requirements —I assume to circumvent a mistake the standard I-Tasser server makes, such as messing up oligomers.
So the hybridisation from RosettaCM (skipping the threading) is probably a good choice, however, requires familiarity with Rosetta.
The model would need to be "symmetric" (oligomer) before starting the hybridisation (Step 2 in the manual). But that can simply be a case of getting the oligomeric template and superimposing that many copies of your threaded model onto it. Then as your threaded model is from a different framework, it needs to be adapted to the forcefield in Rosetta which differs from I-Tasser, so needs to be minimised, using Relax.
Another minor note is that a weakness is the pairwise alignment for all of these, which for distant variants can be problematically erroneous —hence why Phyre2 and I-Tasser run a MSA and from there extract the pairwise, which is a lot more accurate. I do not know how the restraint4 parameter works.
I realised just now that maybe SwissModel was not tried —it is an old threader, but does oligomers nicely. In fact, I tried your sequence and the hexamer looks decent and the internal metric is pretty good...