I am afraid you were given incorrect information; it is indeed possible to upgrade/MFU the inflexible, discounted fares (in any class) using BA Miles.
You can even upgrade Sale fares.
The only exception is that you cannot MFU the 10% off shareholder discount bookings.
It may, however, be that there are only flexible tickets left, which is why you were quoted that price. BA is not running a Premium Cabin (Club/First) fale sale right now, but it is running a Premium Ecnomy WT+ fare sale.
You would be best advised to go for either
1) a full mileage redemption
2) an MFU which has the advantage of earning both points and miles for the trip, but has the disadvantage of costing more in cash terms BUT the WT+ fares are currently on sale so you might snag a bargain.
In both cases you can “open-jaw” the ticket, flying out to one hub (eg LAX or SFO, and returning from LAS or PHX.
There is also some flexibility to mix cabins outbound and inbound. With a full redemption you can mix and match as you please; outbound in F, returning in Y for instance.
For an MFU, you can only upgrade one cabin ahead of the class of service for which you paid, but you can choose also to travel only in the cabin for which you originally paid on one sector. So if you purchased Club World, you could upgrade just the outbound to F using miles.
Note that there is no First cabin on the LAS services.
If you are making a full redemption (BA Miles only) my recommendation would be to outbound in First to your most distant destination as you get to experience the Concorde Room on the outbound (be sure to leave time for this on your connection!) and the full daytime exLHR F experience.
Then return in Club World, when you will be able to sleep on the fully flat bed, and on board experience is less important.