Is there anything that has been tried to stop publication shopping
A version of your suggestion 1. is implemented in my academic field (mathematics).  

In mathematics authors usually pay dearly to submit to any particular journal, not in money but in time. Namely, an unacknowledged but hard to dispute stage of the refereeing process in mathematics is the part where the referee lets the submission sit on their shelf for N months.  It would be interesting to track the dependence of N on various factors, but based on my own experiences as an author (and okay, yes, as a referee!) I believe the median value of N to be about three months, with a higher mean.  Especially, when I submit a paper to a large range of reputable journals in my field, I feel that I am incurring a risk -- small, but not negligible; let's say 3-5% -- that the referee will wait a year or so before rejecting the paper with a wholly superficial accompanying report (say, one paragraph that does not make specific reference to anything in the paper past the introduction).  

This makes it rather impractical to shop a mathematics paper around to a large number of journals at about the right level.  (If you send a less than excellent paper to a truly excellent mathematics journal, the chances are good that it gets bounced back to you quite quickly.  I have heard stories of the absolute top journals in mathematics keeping a paper for a year or more and then responding negatively...but then I have also heard of them doing this and then accepting papers that I would have guessed they would reject.)  This certainly works for me: I have submitted over 50 distinct math papers for publication.  Most often I step down in quality after the first rejection and always after the second rejection.  For me, having three or four journals consider the same paper feels like quite an ordeal....because it is likely spread out over several years!

Maybe this sounds sarcastic.  It is not intended to be.  If anything, it is a relief to think that there might be some good effect of the current endemic slowness of mathematical refereeing.  Because we have a thriving preprint culture, it is hard to argue that slow publication has a significant effect on the intellectual progress of the field.  If only the slowness were equidistributed, I think there would be little to complain about.  (But it isn't, and I suspect that my suffering is as nothing compared to that of some of my junior colleagues...In fact, just now I realize that while for many years now my papers have been treated better by top journals whether they take them or not, at the beginning of my career I had several papers languish in top journals for a really long time.  The rich should have to pay more, not less.)