I work with a community group rebuilding bikes. We do a fair amount of bottom brackets and crank replacements. Never had this problem before then have it twice in one week. One we replaced with a good condition used crank.

The original part 48T crank has some fair bends in different rings so we opted to replace.

First pic shows how the orig part fits. Second is the new one. Both are diamond.

Never had new cranks sit this far our before. Seen some threads on needing to super tighten some cranks but not seeing we can tighten this enough to force the crank on another 1/4". Don't want to try to super tighten and then try to remove unless it's really likely to work. We even tried a new 42t crank but it sits out just as far.

Anyone else have this problem? Are there some brands that fit better than others? Or can you really tighten it enough to fit?

That is just a probably just a poor match-up between the crank offset and the spindle length.

Older cranks were designed to use a longer spindle, or at least longer on the drive side. The symmetrical ones at that time was 123mm or 127mm, or longer.

In the 1990s many cranks were changed to use a shorter stiffer spindle, Shimano's name was 'low profile'. The offset of the interface was moved inward to match the shorter spindle. The symmetrical spindles at this time was in the 110-116mm range.

The common chainline also changed for most 3x MTBs. It went from 45mm, (common for touring cranks that was used for early MTB) to 47.5-50mm.

So, to get the best results, you need to find out the intended BB/spindle that the cranks was intended for.

I'm really generalizing here, but there are two rough generations of cotterless three-piece square taper cranks & bottom brackets.

The earlier ones (1970s-1990s) were designed for road & touring bikes (although also used on early-generation MTBs), had straighter arms, and generally use 121-127 mm wide bottom bracket spindles.

The later ones (1990s-now) have arms that curve outward from the spindle to clear wider chainstays and provide better ankle clearance, and generally use 107-115 mm wide bottom bracket spindles.

As with all parts, variations abound. There is also the ISO vs JIS taper issue which can affect fit & durability.

I'd recommend swapping for a narrower BB and trying that. If the chainrings are making the chainstay lighter by grinding it away, try a slightly longer one.

KCT1986: Jinx!

This shows some (not all) of the different spindles-

to sum up.. you need a different, Shorter, Bottom Bracket Spindle length to fit the "new" Crankset...

and, as someone that works on a wide range of old bikes, there are THREE general square/diamond crank styles.. i call them "Innies", "Flattes", and "Outties"

your old one shown is a "Innie" and they use the length Bottom bracket spindle that is still in the bike... around 123 to 127 mm length...
the new one looks like a "Flattie.. it will, most likely need a 118mm Spindle, but might need a 113mm spindle, depending on the bike's Frame

measure the Frame at the Bottom Bracket.. NOT the Bearing/spindle part, but the FRAME'S Tube that the 4 other tubes meet up at... it will be 68 or 73mm.

now... measure the width between the plates the rear wheel sits in between, and the axle clamps to... that is called the "Over Locknut Distance", or O.L.D. for short... it will be either 126, 130, or 135mm.
126mm and 130mm are road frames, and 135mm is an MTB frame.
(SOME really old MTB frames use 130mm O.L.D., but they are getting more rare by the day...)

report the measurements to this thread, and the bottom bracket spindle length you need can then be determined, ok?

Depending on the model of the new crank, you may be able to just look up what size bottom bracket it needs.

^^^^ What they all said about crank length and ISO vs JIS taper issue

I believe someone above mentioned this link https://sheldonbrown.com/bbtaper.html

set up chain line for what you want with spindle length.

​​​​​​https://www.sheldonbrown.com/chainline.html