Well, the strategy is very obvious. Theresa May decided what the UK side would ask for in the negotiations. It was a package that ruled out what she felt her party's right wing wouldn't like, but included support for the Good Friday agreement. She involved nobody in formulating this negotiating position outside of a small group of right wing leave supporters, although the fact that these all walked away from the process, suggests that it was mainly down to her. She then spent two years (I'll say that again) she then spent TWO YEARS getting representatives of 27 separate countries to come to an agreement closely tailored to her package of requirements.
The strategy simply involves stubbornly insisting that the UK parliament has no role other than to vote for or against this particular package [because she has no intention of allowing any input to discussion of how the UK should leave other than her own] with the threat that if it is refused the UK will get no exit deal or else we will revoke Article 50 and remain in the EU.
An alternative package that includes membership of a (or the) EU Customs Union and/or the EU Common Market without membership of the EU and it's political institutions and other financial institutions has never even been discussed by Parliament or raised with the EU negotiators. This would be hated by the Tory right wing that has a set of values honed on the playing fields of Eton and Harrow and in the drinking clubs of Oxford and Cambridge, or in the case of some such as Mark Francois, a fantasy England where World War 2 never ended. May's strategy here is to ignore the possibility that alternatives even exist.
Quite understandably, having spent 2 years discussing May's package deal, the EU doesn't want to discuss this any more. I have no idea how they might react to starting again from an entirely different place although some politicians who have raised the possibility with EU negotiators say that they might be sympathetic - and certainly this would be closer to a model that the EU is used to with e.g. Norway. There is almost certainly a majority in the UK Parliament for this sort of arrangement, probably a substantial majority, but unfortunately the Tory rank and file seldom show the level of courage required to make this happen. And with May currently stuck on the view that her way is the only way and consequently seeking only a short delay to Article 50, probably no time.
By the way, Bercow's ruling wasn't just the resurrection of some ancient precedent. He was ruling in line with the way parliamentary business is done every day. If a bill is voted down then it doesn't get voted on again in the same parliamentary session without a substantial change. Those who don't like the ruling are trying to make it sound like one of those ancient laws like it's illegal to enter the Houses of Parliament wearing armour.
EDITED: 20 Mar 2019 11:48 by WILLIAMA