Lawman

Midway over your side of the pond - unfortunately discontinued (Bell & Carson)
https://www.midwayusa.com/product/1006748841

It might be a suggestion to directly contact Bell & Carson anyway, they might have one lying around even if discontinued stock
https://www.bellandcarlson.com/index.cfm?fuseaction=page.display&page_id=33

Boyds - laminate stock, in reality it wouldn't be that much heavier than the walnut stock you already have, not unless you're climbing mountains or have some physical limitation or you're are getting towards the end of your hunt career then the extra weight shouldn't bother a younger reasonably fit man.
https://www.boydsgunstocks.com/product-configurator/plat-springfield-1903a3-mbc-4a2841v43zz

McMillian - give them a call it appears they can modify stocks to suit an action
https://mcmillanusa.com/stock/game-warden/

This was only a quick search, others will undoubtedly chime in about this (Ripp here is a big synthetic stock fan) ,there could possibly be a smaller niche synthetic stock maker out there that does only small runs or one of type jobs - if you really decide to go this route.

To me I would get any type of replacement stock available first up if I was super concerned about damaging the original stock & it was going on a hard hunt very soon that would most probably damage it, at least you have peace of mind.

Additionally we do have some good articles concerning refinishing stocks in the archives squirrelled away, should you want to do the refinish/refreshing on your own stock. - but be beware it is addictive stuff when you start reading!

finally
I would be tempted to give Aaron Little a gunsmith here at NE a PM, he would give you solid advice after he picked your brains about what you really want your Springfield to look like; perhaps even to the point of just 'refreshing' your stock so it still looks like in its original form.
If possible post some photos if you can of you old '03, to see one of these stocks done up would make a great piece here as there is always something 'new' like this popping up to see what fellow enthusiast come up with or most probably already done!
Really looking forward to see what you do with the original stock (& its replacement of course)
Cheers
93x64mm