(1) If you add more time, what do you take away? At least start to address this issue.
(2) I agree that there is a huge amount of material covered in multivariable calc, but I fear that your solution of two semesters (adding lots of extra content!) is not even addressing the issue in terms of developing the topics themselves with more practice and familiarity. In other words, you are adding more time, but also more content. How can I tell if this is better/worse? (2 unknowns with one equation.) Why not do something simple like adding more time for the same topics? At least then I know the directionality.
(3) The two quarter idea is interesting in that it allows performing the idea in (2) [deeper practice with unfamiliar and less intuitive topics like line integrals and div/grad/curl and all that, but not adding a bunch of extra content in.] The question then becomes what do you do with the rest of the calc sequence? ODE really could use 2 quarters for the same rationale. If you have advanced students (above average, exposed to strong pre-calc), you could do some quarter sequence like (1) differential calc (2) integral calc (3) calc 3 part 1 (4) calc 3 part 2 (5) ODE part 1 (6) ODE part 2. The extra time for calc 3 and ODE is nice. Disadvantages would be students that really don't know regular calc that well (after all they did not place out of it!) Also, you stretch multivariable calc over a summer. (that said, there are disparate topics.)
(4) I actually think the fundamental topics of single variable calc (and to a lesser extent diffy Qs) are more important to STEM students. Perhaps covering multivariable calc in some less satisfactory manner is sufficient. Sort of how LaPlace transform is covered in a short manner...so that students have at least seen it...but will need to learn deeper within the context of whatever EE or control systems course needs it later. In other words, not really developing competence (as we do with integration methods), but familiarity.
(4.5) The main need for multivariable calc is in E&M. However, the standard physics 1 E&M basically uses line integrals and not that much else (yes, you may vaguely touch a little of it when hitting Maxwell's equations, but line integrals are the main thing for problem solving). It's not ideal, but probably sufficient for the majority of STEM majors (who all agree that first semester physics is like high school warmed over and then second semester is a pain in the butt...but you get through it and move on to other things.) Physics majors really do have a need to do more applied vector calculus, but this is covered very hard (get lots of review AND practice) in the context of junior year E&M, ITSELF. For instance, look at the first chapter of Wangsness (it's one ~80 page vector calc lesson with almost no physics).