I see you are getting your information from Ben Witherington, I have read this also and I can see some of the weight it carries.
I found it to be pretty persuasive when I read it last year. However, I held off judgement until I heard from a more authoritative source.
You mention the issue of the High priest, but let us not forget that the last place Lazarus would wan't to be is NEAR the High priest or those looking to kill him, as the very GOJ mentions.
To the contrary I think it is perfect. It contrasts Lazarus' bravery with Peter's cowardice. This is further shown when none of the other 12 stay by Jesus side during the execution but Lazarus is there.
The issue of whether the supper in John is THE last supper is a tough one since John makes no mention of "bread and wine", Since that was already dealt with before, but it DOES mention Judas' betrayal and the subsequent capture of Jesus.
Yes I agree that the mention of Judas' betrayal does lean toward it being the same the event despite the curious absence of the "bread and wine".
Order of progression is something that the writer(s) of the GOJ didn't focus too much on, or [erhaps the editor(s).
Yeah I'm not sure about the order of things. For instance GOJ places the cleansing of the temple at the start of the ministry whereas the other gospels have it at the end. So you either have the same event happening twice or one account is incorrect.
There are also some weird timing disagreements that I haven't been able to reconcile. GOJ has Jesus being executed before the passover meal while the other gospels have it afterword.