The problem is that Dorico does not currently allow you to define a metric modulation between different meters, so they’re currently always pegged at quarter = quarter, whereas in this case you want dotted quarter = quarter (or, if you prefer, dotted half = half). You can use tuplets to fake the appropriate relationship – there have been quite a few posts on this topic over the years, so a quick search on the forum will turn up lots of results, or you might find this tutorial helpful.
Invoke the caret on the first French Horn stave, then type Shift-M 6/4, 4 Alt-Enter. This is telling Dorico to add a 6/4 time signature with a 4 beat anacrusis.
Duplicate it down to the other Horns.
Add a 2/2 local time signature to the French Horns in the next measure, then hide from the properties panel.
Use ordinary quarter/crotchet triplets for the Horn material, then hide brackets and numbers using the bracket and number properties.
Thanks very much for the help and quick response! Both you and Daniel are on the same track it seems so I’ll follow your directions and hopefully get things moving along.