finishing

I use Minwax poly but I doubt that's your type of finish. Your home-brew might benefit from a hard furniture wax as a top coat. Or you can try Waterlox, an expensive favorite of the more traditional woodworker here.

Waterlox (red can) will give a semi-gloss finish, but can't say if it will play well with the OP's home brew.  A bit of surface preparation might help.  Sanding to a higher grit may help.  After "final" sanding, apply a spit-coat of  1lb. dewaxed shellac; allow to dry well; lightly scuff sand by hand with a next-higher grit paper; vac well; apply the oil finish.  The shellac will increase the reflectivity of the wood surface and allow the oil to level to a higher gloss percentage.
As always, test on scrap before use.

A linseed oil + wax finish is always going to give you a flat-ish sheen.  For satin you really need more of a film forming recipe.

I've used Waterlox original sealer/finish over linseed oil often on walnut and the oil causes no problem.  I believe your wax component could interfere with the topcoat however.  I use Waterlox as a wiping varnish, wipe on a very light coat with a clean and as lint free as possible rag (old sheets work well).  It will even build to a gloss if you do a lot of coats.  Waterlox tends to gel in the can once opened, so I decant it into various jam jars I keep around so that the loss to gelling is minimized.  Open and use a jar of finish repeatedly for a week or two and it's going to gel up on you.  May vary with humidity, it's dry where I live.  If you catch the gelling quickly, a shot of turpentine will reverse it, but that changes the film properties a bit, makes a softer finish.

The wax will be an issue in applying film finishes or anything else, for that matter, over top of it. The linseed oil is the component giving the grain pop, not the wax.
A common do it yourself finish is equal parts of varnish, turpentine or mineral spirits, and oil - (real) tung is often recommended because it doesn't darken with age like linseed. Lots of pre-mixed finishes say tung oil on the label but the amount of tung oil is virtually zero.
Driers may add some gloss so it's worth a try since you like your mix. Follow the instructions, you do not need much drier.
Also, make sure your bare wood is well and evenly sanded - an unsmooth surface will degrade the chatoyance.
I find the recommended sanding grit to be somewhat coarse but they often refer to good absorbing. Some woodturners will commonly sand to 1500-2000 before applying film finish.
There are ways to prevent or at least slow-down finish thickening:
My favorite now, is a Stop-Loss bag.
You can also put the finish into a smaller can so there is no air (oxygen) space.
You can add marbles to finish to achieve the above.
You can water to oil finish to achieve the above - it sinks to the bottom like the marbles.
You can use Bloxygen (argon gas product) to remove oxygen.
I've heard of CO2 from pellet/paint gun cartridges being  used too.

Thanks everyone for responding. I'm trying increasing the resin to add hardness,
will also try a small amount of Japan dryer. I do heat the mixture to melting
point for good penetration. The mixture does seem to work better, higher gloss,
on darker woods like mahogany. 
Thanks again.