I have not done the Tek Cave before, however I find it extremely doubtful that you will have enough time to kill the overseer with your dinos. It took me 10 minutes to kill the alpha dragon with mate boosted fully imprinted youth boosted level 350+ boss therizinos with all points in melee. You have (correct me if I’m wrong) 30 minutes to kill the overseer. If you take 7 carnos in, that are not imprint boosted by the rider (all of our theris where imprinted to the rider) you will loose about 30% damage output from the carnos. Also, if any of them are wild tames, they don’t get the general stat increase from imprints, which is another 20 % (i think). Furthermore, the base damage on the theri is higher (52 vs 35). So if you factor in the base damage difference and the imprinting difference, the time would likely run out before you killed the overseer.
If you posted the stats for the Carnos I could make a more accurate prediction about this, but in all the boss runs I’ve done, the rexes take a pretty sizeable amount of damage. When doing the dragon, some of the theris got down to below 3k health from 13k, and we where using veggie cakes. So secondly I don’t think the carnos are tanky enough to survive the overseer and all the defense units and crap that is spawns.
finally, I didn’t see you mention what the armor on your saddles is. I would highly recommend at least 90 plus if you are gonna do a Tek Cave run.
So here are my recommendations: bring either rexes or therizinos in place of the carnos, they are just simply not tanky enough and don’t deal enough damage. The yuty buff does make them less likely to die, but trust me, they buff works just as well on rexes and theris. I’m not saying you shouldn’t bring in the diplos, they could theoretically deal with the giga. However I have found shooting him and then kiting him into the lava to be the easiest way to deal with the giga. Also, you can take up to 50 dinos into the boss, so bringing 7 carnos, 2 rexes, some diplos and a yuty are really light, your gonna want a few more dinos, I’d recommend at least 20 for rexes and at least 45 for carnos. I would also take a yuty in reguardless.