"Closing" issues, when hand-cycling rounds in the gun? Really?
Some thoughts ...
Don't use live rounds for bench checks. Use properly sized Dummy rounds.
Dummy rounds not only help prevent a potential "mistake" (negligent discharge), but prevent unnecessary damage to live ammunition which could compromise functioning at the least (case rim damage, extraction& feeding failures, etc), and may create the potential for what's sometimes called an "over-pressure event" due to bullet setback (think catastrophic failure that could damage the gun and/or injure the shooter - perhaps seriously or even fatally).
Don't compare how a particular pistol may feel when "slowly hand-cycling it". It's intended to work that way. It's intended to operate normally when being fired.
Don't compare how a compact pistol with a slightly shorter slide & barrel may function, mechanically, from a perspective of "leverage" while cycling, to a slightly larger version (even by only half an inch).
Don't start taking files to extractors. Really. This isn't a 1911. The hooks aren't filed, stoned or otherwise "adjusted" by technicians or armorers when being installed in guns. (They've been revised a bit over the years to offer optimal feeding, using a wider range of commercial ammo, though.)
The only filing that typically needs to be done is on the adjustment pad (and this filing work is checked by use of a Go/No-Go bar gauge, not Dummy rounds, shaking the slide, etc). There's a rare exception involving some extractor tails in some of the oldest 3rd guns, maybe, but I've never talked to another armorer that ever ran into such a gun/extractor combination. It's just been mentioned in passing during some earlier armorer classes. Not the hooks, but a spot on the tails.
Don't start changing extractor springs unless you know what you're doing, meaning you have the knowledge, training & experience ... and you have actual reason to do so. FWIW, just because one aftermarket spring maker may measure the tension of their springs using one method, applying a "weight rating", that doesn't mean that's how S&W applies ratings to their springs (also supplied by a vendor).
S&W has a recommended tension "weight" measurement for checking the tension of the pivoting extractors used in their 3rd gen guns. The "weight measurement" they use is checked with a force dial gauge, checking for a reading at the first sign of deflection of the extractor when placed under load (using the tool they sell to armorers). The recommended spring tension can vary within an expected range, and some optional springs are available to armorers to help get any particular pistol within the normally recommended range. This can allow a repair tech, gunsmith or armorer to resolve some issues that might occur with a particular pistol (meaning tolerance stack among various parts in a specific gun), and taking into consideration the influences presented by any particular shooter and ammunition combination.
A spring which provides too much tension may cause feeding problems, and one which is too light may cause extraction problems.
Older slides had their extractor spring holes machined by equipment controlled by an operator, unlike the newer CNC equipment (which can also be self-regulating in identifying a dulling cutter, whereas the older equipment relied on the operator being aware of things). That may result in some extractor spring holes varying a bit in dimensions, such as depth of the hole and/or the shape at the bottom (which can change the "tension" of a spring if it has to be compressed more in one slide than is typically expected).
Of course, even the newer TSW guns, built on the latest CNC equipment, may have the occasional manufacturing hiccup occur. We had a TSW slide (a .40 gun) that just wouldn't give enough tension for the extractor spring, checking it with the dial gauge, when the standard production spring was used, even when a couple of those springs were tried. Failures-to-extract occurred (which is the reason it came to my attention in the first place), and the spring tension fell below the minimum recommended reading for the different "standard" springs.
I ended up having to use one of the heavier optional springs to resolve the issue. The heavier spring resulted in a reading which fell within the normal tension (weight) range, and the gun fed, fired, extracted & ejected as intended afterward. problem solved. The extractor had been fitted just fine, but the "problem" was caused by an extractor spring which gave insufficient tension in that gun.
I've previously run heavier recoil springs in 3913/6906's. Some thousands of rounds to see how things ran using heavier springs. I no longer do so. Many more thousands of rounds using factory springs have given me enough reason to stay with the standard rated recoil springs sold by the factory (very affordably, I might add). I use the standard factory recoil springs. Ditto mag springs in the single column 39XX guns.
When you start changing the springs the engineers designed to be used in the guns ... and especially when you think about breaking out files to "fix" something ... you may risk experiencing less-than-optimal functioning & operation.
No reason to "fix something until it's broken". Really.
If you do something to ruin how the gun works, meaning how it's supposed to work (not just according to something you may like to feel is normal) you'll have to pay either a gunsmith or a factory tech to repair your "fix". That doesn't take into consideration the potential for frustration, as well as what might happen if the gun actually doesn't safely work as designed when you're shooting it at the range, or may desperately need it for a defensive situation.
Presuming the 3913 is in normal operating condition (not visibly damaged), the recoil & magazine springs are in good condition (I'd replace both in any used 3rd gen gun I bought, myself, using factory springs as the replacements), and the gun is properly clean and lubricated ... I'd shoot the gun with fresh factory 9mm ammunition, made by one of the major American ammo companies ... and if it feeds & functions normally during live-fire, I'd leave well enough alone.
Just my thoughts. I'm an owner & shooter of a late production 3913, myself, as well as an armorer for 3rd gen S&W's (4 classes, meaning some recerts to keep current).
Congrats on finding a low-mileage 3913. Outstanding compact 9's. Easily among the best models S&W has ever produced, if not the best.
