No, you can tell Notation Options to prohibit pitch crossing, then set a Condensing Change where you want it to start a new phrase and allow pitch crossing, then set another Condensing Change and turn off unlimited pitch crossing.
As to why stuff on another system or another page affects the way Dorico condenses this system/page, let me quote a lengthier post I typed yesterday:
The most important consideration is that Dorico handles Condensing a phrase at a time, where a phrase is defined as everything between simultaneous rests in all instruments within a Condensing Group (and at least one rest that isn’t within a tuplet).
That’s a lot of words to take in, so here’s an illustration:
As you can see, in each case Dorico has to take the approach (regarding stem direction and labelling) that will work for the whole phrase, but only that phrase. If the phrase happens to start with a note in one instrument and a rest in the other, Dorico has no choice but to present the whole phrase as two separate voices. At the next set of rests, it can take a different approach. Keep reading for a way to force a new phrase despite the absence of rests.
As in general with Dorico, the fastest approach is to set good global options, and then override them locally where necessary. In this case, Library > Notation Options > Condensing is the place to set the global options, and Engrave > Condensing Change is the place to locally override.
There are all sorts of things that you could do in the Condensing Change dialog, but in cases such as the one in your screenshot, all you need to do is tell Dorico to start a new phrase at the start of bar 92. You can do that by - in Engrave mode - selecting something at the start of 92 (a note, a dynamic, a barline), then Engrave > Condensing Change , then tick the relevant players in the left side. Ticking nothing else at all will force Dorico to consider bar 92 as a new phrase:
It’s well worth reading the documentation on Condensing Calculations and Considerations and scrolling down through the Condensing Results section too. My point about introducing Condensing Changes to start new phrases is mentioned in a Note in that section.