What is the best method to write this?
I got this far by setting 2/3 and using hidden triplets;
Is this the correct/best method?
Can I get ( ) around 2/4 ?
Yes, I think this is your best bet.
For brackets, this might help:
If you have a project with lots of staves, don’t forget to make it system-attached text.
In fact, if you use @dan_kreider 's suggestion about the MusicGlyphs font (which is fantastic), you could just create a 2:3 tuplet in the “2/4” bars.
It’s easier to leave the outer staves in 6/8, so you don’t need triplets. Just put a local 2/4,3 on the middle staff, and then on the next bar a local 6/8 on the same staff and hide it. Then you only need hidden duplets (or 4:6s) on the 2/4 staff.
Won’t the barlines for the 2/4 bar not align with the 6/8?
When you write 2/4,3 that means show 2/4 but with a 3-quarter pickup bar. Then you silently put it back in 6/8 in the following bar, so all the barlines still line up.
Gotcha
It seems to not work this way for the local time signature? Unless I’m doing something wrong
Edit: Don’t worry - I’m a fool. 
The 2/4 is just for show, of course. Since it needs parentheses, it’s probably just as well to do it as text and space it manually, like you said above.
I tried this but got bar numbers in [ ] in all the following systems.
Edit: It is correct now. Don’t know what happened.
It seems to me that these answers are best for a few bars in 6/8. But if the entire player is in 6/8 while the other players are in 2/4 this would mean fussing with every single bar. That’s not optimal.
Welcome to the forum.
6/8 against a general 2/4 is really quite straightforward.
- In the first bar use shift-M 6/8,4 (alt-enter) - this creates the independent time signature and keeps the bar length at 4 quavers.
- In the second bar shift-M 2/4 (enter) - returns everyone to the global time signature. You then hide it using properties.
- Now you just enter all the notes in the 6/8 part using tuplets. (There are engraving options to automatically hide the tuplet numbers and brackets for repeated tuplets).
But you have create that Shift-M 6/8,4 mickey mouse for every single measure! Neither R nor Ctl/C (copy) duplicates that measure’s time properties.
NO YOU DO NOT! (sorry for shouting).
You only use it for the first bar (and it is only needed to show the initial time signature)
Then the bars won’t line up.
Oh yes they do if you follow the three steps I detailed.
As I explained, the first time signature creates a shortened bar with the correct time signature (the bar is the same length as a 2/4 bar so the barlines line up).
The second time signature (which you hide) returns everyone to playing in 2/4 (so again, all the bars are the same length and the barlines line up).
The only “inconvenience” is you have to enter all your notes on the 6/8 part as tuplets, but often that’s just a matter of turning on the tuplets and adding the notes (extra tuplets will be created when the current one is full)
That kind of defeats the point though, no? If they’re still notated as tuplets and quarter notes instead of eighth notes and dotted quarters, then it’s not really 6/8. How do you get it so that the 6/8 is notated like 6/8 with tuplets and dotted quarters?
If you follow the instructions given by @janus, you get this:
Isn’t that the look you’re going for? It’s true that the top line is entered as tuplets (since Dorico thinks there only 4 eighth notes in the bar), but then you just hide the tuplets.
Yes, they just mention “there are ways in engraving options” to get it to look like what it’s supposed to look like, but I don’t know what those are. How do I get a measure that has the time signature of 6/8, but actually is in 2/4 under the surface, to have a dotted quarter note plus three eighth notes?
There are two separate things here. The first is how to get the time signatures right; the instructions for that are given in @janus’s post.
The second is how to hide the tuplet numbers and brackets. If you want to absolutely hide all numbers and brackets, then go to Engraving Options > Tuplets > Repeated Tuplets, and set the first two options like this:
Note that this will also hide the bracket and number for legitimate tuplets that you have in the 2/4 staff. Otherwise, you can select individual tuplets in the 6/8 staff, or select a range of music and filter to select only tuplets, and then use the lower Properties panel to explicitly hide the number and bracket.
(If you hide them all in Engraving Options, you can also use the same Properties settings to explicitly show some tuplets.)
This is just two eighth note triplets, and then hide the bracket and number.