If you are worried about revealing the SE (thus alerting your opponent to your plan and incentivizing them to stack favorably) by asking opponents to specify the order of their triggers, I think there are some sneaky ways you could go about fishing for your desired outcome. For what not to do, maybe something like, “hang on, how are you ordering your triggers? Because I might have a response.”

I think feigning confusion would work better, e.g. putting your hand down and saying “sorry let me see if i understand this: he’s going to die, but then you will get to draw a card and gain life right?” When your opponent inevitably confirms, they are locking themselves into the order demanded by Surgical and you can say “okay, then I’ll respond to the draw a card trigger now that Uro is in the graveyard.” Many opponents probably won’t even feel tricked!

From what I can tell, the problem is (ironically) mana and durdle. Astrolabe smooths out a lot of the problems with playing a 3-color manabase with a lot of basics, but can’t eliminate them entirely. The mana can be awkward to the point of lethality in Temur and Bant as-is, so mixing them is a greedy proposition.

Then there’s the issue of space. Snow that isn’t Snowblade tends to be very durdly, Temur more than Bant. Wrenn is a good card for helping mana, but doesn’t do much by itself. What you’re proposing is a deck with a whole lot of control, and few ways to actually win. I wouldn’t rely on opponent’s conceding as a win condition.

It’s odd to me that 4c doesn’t see as much play as Bant or Temur. Wrenn’s a fun card in Jund so I might be biased here, but she seems too good to not play. Getting back fetches would be helpful for fixing when you don’t have Astrolabes (or when Karn turns them off), and for fetching Mystic Sanctuary later on. Plus she works well with Jace Brainstorms (the hidden extra cantrip in the deck). White obviously has Teferi and Path even without running Stoneforge, so combining Bant and Temur looks like the way to go imo.

So the short answer is that under the rules the trigger’s controllers must select and specify the order. If they fail to do so, this must be corrected and specified.

For the real meat of your question, that’s an interesting area. To the best of my knowledge, and I should remind you I’m not a real judge (I just play one for FNM), there is no assumed order, though in general judge instructions are to default to the interpretation favorable to the trigger’s controller. Thus if there’s a question, they’re likely to not give you the ruling you want if there’s ambiguity.

However, actual play actions take precedence over assumptions, particularly at comp REL or above. So if your opponent plays said titan, moves it to the graveyard and then tries to resolve the other trigger, they’re considered to have specified the action by demonstration, and your plan will work. I don’t know any real judge that will let them take back such an action because they demonstrated the effects of the triggers in an order. If they do the action first then move the titan to the graveyard, they’re out of luck. Now, in my experience in paper most players will resolve the ETB value trigger first by default action, so it’s unlikely to ever work in the situation you’re asking about. However, there will be a few times when it will happen, so you need to keep your eyes open.