Additional layer of protection over polymerized linseed oil that maintains feel

Ideally looking for something that maintains the natural feel of the wood as much as possible while also protecting it more than linseed oil does alone.

Linseed oil in general provides very little in the way of protection to wooden surfaces, even when many coats are built up over some time and then allowed a full curing period — more than a month — as with the traditional procedures.

So it is quite easy to add protection here, since most other finishes are more protective.

Maintaining the natural feel of wood is harder, since everything changes the feel somewhat. Plus there is some subjectivity here (read: a lot for some people). But once you have applied linseed oil maintaining much the same feel as that is a lot easier.

One of your simplest options here is to wipe on polyurethane varnish. When wiped on poly becomes one of the easiest finishes to do well..... for all intents and purposes it's the same as applying linseed oil. And the protection it provides is streets ahead of linseed, even polymerised linseed which is quite different to raw linseed oil or "boiled" linseed oil. See this previous Answer for more on making your own wiping varnish and how it may be applied, the info from finishing guru Bob Flexner who has done more to popularise wiping on poly than anyone else.

If using the option to wipe away all of the excess (which I would recommend here for a couple of reason) I suggest applying at least four coats, but six or seven would be better if you can stomach the time it takes.

Note 1: remember that full protection is only afforded once a finish has had a decent amount of time to cure, which here will be somewhere about 3-6 weeks after the final coat is applied.

Note 2: if you end up with a surface that feels a little slick a light sanding with fine abrasive paper (320 or finer), or scuffing with fine steel wool (0000/00000) or fine ScotchBrite will sort this out and even up the reflectiveness of the surface while you're at it.