You could replace the i7-3770 with an i7-3770K, then go into the BIOS, select Advanced, AI Tweaker, Turbo Ratio, By Per Core and increase the multipliers. I could go downstairs and boot up an old rig which I believe has a K-series 3770 and see what its overclock settings are.
You should be able to set x40 multipliers all-core, possibly higher, but use a big heatsink. I don't run older 1150/51/55 CPUs above 1.250V (manual Vcore). High overclocks can push Vcore over 1.40V (on Auto) which can kill your processor. Take care! If the machine is vital for work, don't overclock.
https://forums.tomshardware.com/threads/overclocking-i7-3770k.3758391/
GT620 definitely isn't plenty for it, app runs at like 5fps.
Are you sure the apps are limited by the GT620? I would expect the CPU to be the limiting factor.
What Operating System are you using? With an off-line CNC machine, it might be Windows 7, given the age of LGA 1155. Nothing wrong with an old OS on old hardware if it's not connected to the interweb. I still have some XP systems for old scanners.
I seem to remember you needed at least a GT630 to fully support Windows 10. Your GT620 might be running as a Windows Basic Adapter display which might explain 5fps if your OS is Windows 10.
I run GT730 cards in LGA 1150/51/55 systems for Windows 10 compatibility, but I also have a GTX 1080, two RX 570s and two Quadro K4000s in similar old builds.
What about the gpu should we just get a gtx 1060? Would the MBO support something newer than that?
The user manual states your mobo supports PCIe Gen.3 with a 3rd Gen CPU, so you should be OK with a modern GPU, provided the card drops back to PCIe Gen.3 from its default Gen.4 or even Gen.5. I prefer to match old mobos with old GPUs from the same decade.
You'd probably need a new more powerful PSU for a big GPU requiring separate +12V PCIe cables.
"Expansion slots
1 x PCI Express 3.0* / 2.0 x16 slot (blue at x16 mode)
1 x PCI Express 2.0 x16 slot (black at x4 mode, compatible with PCIe x1
and x4 devies)
2 x PCI Express 2.0 x1 slots
3 x PCI slots
* PCIe 3.0 speed is supported by Intel ® 3rd generation Core TM processors."
There's also the question of graphics card drivers. If you're running Windows 7 or XP, a modern GPU may not have suitable drivers for out-of-support Operating Systems.