IIRC, these have a reputation for poor accuracy.
What, exactly, seems to be the problem?
(I wound up with one that shoots patterns)

I usually add a tension screw to the forend hanger.
Have you tried shooting it without the barrel band? If I have a no 1 or no3 that needs tuning I usually remove the forend and try for groups. I also use a wedge between the barrel and hanger pushing it in deeper looking for a sweet spot. If I find that helps I drlll and tap for the tension screw. Or you could try the Hicks device. The forend is another place to look. I have slightly relieved the barrel channel and where it touches the receiver. Usually the tension screw has done it for me.

Your memory is very good.
Ruger #1 and 3 have a reputation. Some say “they can be made accurate”, some say they can not. I’m in the latter camp. Have owned five of them, all #1, all small caliber stuff. Four could not be made to shoot anywhere close to an inch, despite various forend pressure, floating and other schemes, and expensive trigger replacements
I did get a #1 in 218 Bee to shoot close to an inch after floating the forend, and replacing the trigger with a Jard 2.75 pound pull.
Good luck.

i have some very accurate #1`s and some that are just ok , i do know how to bed and float #1`s that can make them shoot better . good handloading can make a difference too. lately i have a been loading Hammer bullets and have had some great groups with this brand bullet ,in my single shot 6 BR bolt rifle and a couple of Ruger #1`s too .

I've owned a half dozen #1's (2 now) that have all been solid MOA guns. A couple #3's in the past shot pretty good too, both .30-40's and both only shot with mid-range cast loads. Used to shoot CBA competition with the one.

Issue is probably with the forearm. Have you tried it with the forearm completely removed? If so, and accuracy improves, then try hanger tensioning tricks and look at the inletting and if it binds against receiver (it mustn't).

Light barreled single shots are particularly prone to accuracy issues if there's contact at the receiver. I always fit them so there's a hair of light that shines through the gap, but still look tight.

I have heard all of that before. I take it with a grain of salt same as older Ruger 77’s dont shoot. My# 1v 223 will shoot little bitty groups time and time again. No problem shooting tacks, my 257 Rob started out as a 3” gun now shoots under a 1” and could possibly even smaller with some load work. My # 3 30/40 was a 1” shooter from the get go. My #3 hornet shot a inch to inch and a quarter. I never did any load work or modifying to it. My 220 was a 3/8” with the first load I made.
Getting ready to start on loading for 3 new to me #1’s
Im sure a bolt gun is on average a more accurate platform but just like #1’s, bolts can take some work to make them shoot.we read about those here all the time too. I imagine Im just luck to not have gotten a #1 that makes me throw in the towel but I will keep trying to find that one, for me its fun

I will have to locate the target, but my #3 in 223 will shoot some loads great, others not so great.

The factory Federal 50 grain tipped varmint ammo shot 1”.

55 gr blitzkings with PP Varmint shoot 1”

64 grain Gamekings with CFE223 shoot 1-1/2” and is my deer load if I use that rifle.

55 gr Soft Points that shoot awesome in my Rem 700 shoot like crap in the #3.

There are no modifications to the rifle and thats with the barrel band in place. Scope is a 4x fixed FX-II.

Yep. Pretty hard to make blanket statements, pro or con, about any one operating system. And sometimes it just boils down to luck. Perhaps I've been lucky with the Ruger single shots I've owned, perhaps not, but I don't care - I like them and have fun with them regardless.

Kinda of like taking the prettiest girl to the dance, she will probably have some (kinks) that need worked out. However she is still the prettiest, kind of like a no 1

Had 3 #1’s and a #3 that did not shoot well initially. Did a little glass bed on the forend hanger and relieved the barrel channel a bit. Bingo! Sub MOA all day.

I have a pure stock No.1B, .22 Hornet that is very accurate, scary even.

Out of 3 #1's and 2 #3's, this is the only one that doesn't shoot well.
IIRC, JB did an article years back, on "tuning" the Ruger single shots - but darned if I know where to find it.

Also, IIRC, the #3 in 223 was the most problematic, for some reason.

Never dinked with a #3.

I will say that my #1A 7x57 is a 1” to 1-1/2” rifle. Last time I bothered with a group, it put 3 175SGK’s in about 2.25” at 200 yards. It is about a ‘01 model rifle, so no Wilson barrel concerns.

The .45-70 is at least as good.

That said, I only bother with 3 shot groups out of either of those rifles and have never seriously tried to make them 5 round sub-moa machines. That’s not what they’re used for so I’ve never bothered. My biggest complaint about both rifles is the lack of a decent recoil pad.

I might feel differently about a 1V .223 or .22-250….

I have a #3 in 223. I relieved the wood from touching the action, put some bedding at the for end and
have a hard plastic shim jammed in between the hanger and the barrel. Did not shoot well before doing
these things to it (#1 in 7x57 done same way).
It shoots Nosler 40 gr BTs, Barnes 45 gr TSX and 63 gr Sierras best. Everything else shoots more
of a pattern than a group.

The trigger could use some work, but it is good enough to hunt with.

Currently loading 40 BTs and 65 gr Sierras for hunting bullets for varmints and deer.

I had a #3 in full factory form. After relieving the forend by sanding the rear so it didn't touch the action it shot 5 shot groups that were consistently around 3/4 inch. My Number 1V would shoot 5 shot groups that were about 5/8 inch. Finally got rid of the #3 because it was clunky in the factory wood and plastic butt.