Giggs as manager worries me. It's a gamble and a half.
Be better than LvG though, at least.
I totally agree with this - but there is another option
Go all out for Pep for next season, and actually tell Giggs he has a 6 month contract to get the team back into (preferably top 3 , to avoid CL quali) but top 4 for definite.
Be open with Giggs all along, and say - you have this long but after that we want you to build experience else where before coming back in 5 - 10 or how ever many years (if elsewhere goes well).
Admittedly this could backfire as Pep is unlikely to come if Giggs were to fail top 4 spot (although not definite, as the club itself is still a big enough draw from a managerial point of view, and might even be a bigger draw if Pep WANTS to complete a total overhaul).
Mourinho is a good option, but I am VERY worried about how severely he may de-stabilise Man Utd as a club similarly to how he did to Chelsea this time around (esp Eva Carneiro situation, which he got critically wrong).
Either way Utd HAVE to make a change before 1/2 way point / before Jan window starts preferably - as morale appears so low, its going to take a bit of time before results take a big turn (if they do at all).
edit - I don't think the Di Maria situation is all LvG's fault, I honestly don't think the player suited the Premier league, it was also pretty evident the player didn't put his all in every match , and while it was near the end of the season the red card vs Arsenal was 100% the players fault, and being a mature player he should have known a lot better. Just one example of his attitude being completely off for most of the season. LvG was also clearly at fault playing him in random positions etc and not getting the most out of him.
Just like this season a lot of cases of incomprehensible starting XI's / sub choices and not playing the best players in their best positions when possible.