I agree, it would be very short sighted to "waste" this team by replacing Papi with Panda straight up. It would also be stupid to sink 120M or whatever it takes into an aging DH and still end up with a sub-replacement level 3B against LHP. There's no guarantee Moncada is ready to go in 2017 to bail you out.
I think you're putting too much emphasis on Shaw and Sandoval as the only options necessitating a need for outside help.
1. Brock Holt has a slight reverse split for his career, though this year he has a pretty massive normal split in a very small sample. If his numbers revert to normal he's a .700 OPS 3B option that will already be on the roster.
2. In the Hanley to DH, Sandoval to 3B, Shaw to 1B alignment there is still room for an extra bench guy along with Holt to take time in the mix. Josh Rutledge for example will likely be back and over rather small samples the past three seasons he's posted LHP lines of:
2014 - 90 PA, .840 OPS
2015 - 26 PA, .748 OPS
2016 - 19 PA, .859 OPS
Very small samples to be sure and he's lost most of 2016 due to injury, but his across all levels LHP splits for the previous two seasons?
2015 - 139 PA, .874 OPS
2014 - 110 PA, .929 OPS
3. Beyond Rutledge the club also has Jantzen Witte, a 26 year old (will be 27 next year) 24th rounder from the 2013 class who, in part due to his age, has been pushed through the minors quickly but has hit well along the way, especially against LHP. His LHP splits:
2016 (AAA) - 83 PAs, .847 OPS
2015 (AA) - 72 PAs, .970 OPS
2014 (A) - 64 PAs, 1.121 OPS
2014 (LoA) - 62 PAs, 1.049 OPS
I'm not arguing that Witte is a real prospect, but he's going to be entering his physical prime, has hit throughout the minors while being on a fast track, and has especially hit LH pitching. I mean, using him as one of the options for a small side platoon role is exactly what you hope to get when drafting someone like Witte and all signs point to him being on track for deployment in such a role come the start of next season.
4. While Sam Travis was derailed with the ACL he was on an extreme fast track last season and is a highly advanced RH bat. He might not be ready for opening day but I would expect him to start in AAA and if he rebounds well he could be pushing for time at 1B very soon.
5. Blake Swihart is still out there as a recent top 25 prospect in all of baseball and prior to his trial in LF the consensus move off of C for him was to 3B where his strong arm could still give value. The club could re-visit that and enter next season with a Leon/Vazquez catching duo and Swihart working at 3B, able to move back behind the dish in a pinch, giving some PH/PR flexibility in close and late situations. This is more of a stretch than the other two, as you wouldn't want to move Swihart only to then move him again to make room for Moncada shortly thereafter, but if the vision for Swihart is as a utility guy he could find some real value by being able to run up both foul lines defensively (C, 3B, LF, 1B, RF) and likely has the athletic tools to do exactly that with a bat that makes him very intriguing in such a role (switch hitter who is naturally RH and has his best splits against LHP).
The in-house options are actually pretty expansive without even getting into when Moncada would be ready, though I doubt it'll be too far into 2017 before Yoan is making it hard to keep him in the minors any longer. He's as rare a talent as we've seen come through the farm and we've all watched Bogaerts, Betts, and now Benintendi burst onto the scene.