Is there a better or faster way to breed a recessive trait into another breed of rabbit?

A project I have wanted to complete for a very long time is to breed the Rex fur characteristic into Flemish Giants, or breed the size of Flemish Giants into a line of Rex rabbits.
Rex rabbits have no guard hairs, and the fur is about 3/8th of an inch long, feeling very plush, but with an adult Rex weighing about 7.5 lbs, the fur is small to do much with, or will take a lot of them.
A large bodied bloodline in Flemish Giants weigh near 24 lbs, with + 18 lbs, not uncommon.

I know a bit about genetics but am looking for another view.
My thought is to breed a Rex buck to a Flemish doe, from that F1 litter mate a bro and sis together and 25% of the resulting F2 generation will have Rex fur, 25% will be pure Flemish fur, 50% will be Flemish fur but recessive to Rex. The trouble is, I will only be able to see the Rex characteristic in the ones with Rex fur. The recessive and the pure Flemish will look alike.
So I will take two does from the F2 generation that show Rex fur and breed them to a Flemish buck, then mate a bro and sis from the F3 generation together and 25% of the F4 litter will show Rex fur characteristic.
Mate two of the rabbits with Rex fur from the F4 litter to a Flemish, then a bro and sis from the F5 together, and 25% of the F6 will have Rex fur.
Repeat until I have a line of Rabbits that are the size of Flemish Giants but have Rex fur.

Is not likely that I will have an animal with less that 100 Flemish bred into it that will be the same size as a Flemish.
With the current model I outlined, this would take about 14 generations to breed 100% Flemish into the animal I outlined. (I already plan on using multiple Flemish lines to reduce doubling bad characteristics as much as possible)
Having to mate every other generation together with itself so the recessive Rex characteristic will show, doubles the number of generations needed to bring in the amount of Flemish genes for size that are needed. But with the Rex trait unseen in the recessive 50%, I do not see another way.

Also, I will start and end with all white Rabbits.

I will maintain two lines for a few reasons, to reduce inbreeding, every few generations cross the two lines and start two new lines.
Sometimes accidents and things that should not happen, do happen, and so I do not have to start all over again, have a second line.

If your only going to complain about the inbreeding/line breeding, find something else that is constructive to do, there isn't a breed of domestic animal that was not started this way. I am going to do all I can to bring in new lines, and remix existing ones as outlined above.

Any and all constructive comments will be appreciated.

It will be sometime before I am able to implement this project, I do not have a place to carry this out at the moment.
The reason I would like to carry this out is I have raised rabbits in the past, and the hides were about worthless.
And yes, I raised Rex rabbits, they were to small to do much with. Some Rex weigh about 9 lbs., but those are few and far between.

I am aware that the F1,3,5,7, etc generations are all homozygous, and all carry the recessive gene.
If I mated an animal with Rex fur from the 2, 4. 6, 8, etc generations to three that do not show Rex fur, in one of these generations, at least one of them theoretical should have the recessive trait and have some Rex bunnies.

This would allow me to know of an animal that is recessive for Rex, but if it will shorten the number of generations needed it is not apparent to me.

This would be one more generation, and if this could reduce the number of generations in the long run, it is not immediately apparent to me, but I think this may be useful. If there is a way to use this method to reduce the number of generations, please let me know.

Just as it takes a lot of scores of 100% to bring a grade of 0 on a missed assignment back up to 100% it will take a lot of generations of breeding 100% Flemish into this line, to bring the % of Flemish blood up to 100%.
It is unlikely that anything less than 100% Flemish blood will be the size of a Flemish.

Thank you for your time, Todd
I just thought, there maybe something I am not seeing or another method.
I am gathering that this is the shortest best method!

Again, thank you for your time, Todd
 
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