Mut I guess I could fix some reel tape to something solid.
For SOT23, the problem is getting the tape stuck to a block/base. I have found that doublestick tape will protrude through holes on the bottom of the tape and cause failure of vacuum pickup of probably better than 1 in 20 parts.
I have milled a slot into a piece of HDPE to fit the cut tape, exactly. Then you can 1. screw a cover plate of FR-4 over it. You can mill/file a window in the cover plate barely wide enough to expose parts but to still hold down the edges of the cut tape (this helps prevent a bunch of parts to jump out if the tape gets hit; it has to be solid). Adjust tension so you can slide the tape through one end. (If it has the clear plastic still on, you can continually advance the tape by pulling on this cover.)
Or 2. you can make a "cut tape vice," by screwing a strip of FR-4 down so it just clamps on the top part of the tape, as long as you are using CNC pickup that isn't going to miss and disturb the tape.
To store a lot of parts, you can load used cut tape by taking the metallicized ESD bags and use a heatsealer to make a number of sleeves into it. Slide the cut tape partly in and start loading it up. Slide it into the sleeve as you go, and the part can't fall out. You have to get the fit just so, but it's not that particular.
Possibly my greatest invention for handling loose SOT parts, for packing your tray or tape block:
The orange bit is a "primer loading tray" or maybe a "primer flipping tray," which is sold from amazon/eBay and/or gun/reloading sites. It's used for flipping ammunition primers. It has little ridges in the bottom. So you just take the parts that are already rightside up, then when those run low/out, you give it a little shake and continue.
If you are going to build one, things that might not be obvious:
The orange tray is hot snotted to another plate of HDPE underneath to give a flatter surface.
The balls are 1/8", and the simple race is milled with 1/8" end mill to be just a hair over 1/8" wide and just a hair UNDER 1/8" deep. Then the top plate just rolls over it.
It might not be obvious, but you have to make the race small in diameter. If you tried to put the race all the way around the outer circumference of the plate, it won't spin freely. (You can see where I tried that, lol.) The mass and relative velocity of the balls will be too high (and more collisions between the balls, but that is probably secondary). Small clearance is what prevents the top tray from tilting. Also, don't fill the race all the way. It looks like I have lost a few, but it works better that way.