Hi Tyler,

OK, each one in turn.
1) Benefits of your upgrade: I didn't see any data in the 'before' condition, and I think in your video you have only measured after? So difficult to say, but you are currently in a modest DIY machine territory. For reference technical papers mention commercial machines of 50,000 N/mm upwards if I remember correctly . . .

2) Wheel upgrade to linear rails, plus steel beam: The linear rails upgrade may not show much stiffness, as they are probably not the limiting factor. But they will reduce the maintenance, and may reduce the vibration a bit. But when combined with the steel beam it will start to help.

3) You can post my reply on YouTube if you like. Just reference the 'mycncuk' forum for the source.

4) You can link to the calculator, again quoting the 'mycncuk' source for the reference. Just one thing - I wrote it many years ago to help myself out with some decisions. I have a Mechanical Engineering background so these calcs are OK for me but I really do not have time to explain the calculations or theoretical background for the worksheet. There are instructions on how to use it contained on the sheet but that is all I can offer. Hope you can understand.

5) Measuring force/deflection around the structure: The only one that matters is the force/deflection at the collet (or tool if you want), and ideally with the spindle in the middle of the gantry and at some depth away from home to represent a cutting position. Force/deflection at other locations doesn't help any. But what does help if you want to explore is keeping the force FIXED at the collet, and measuring deflection at other parts of the structure. This will build up a sort of deflection map of the structure and show you where in the chain the worst deflection is happening. Keep the force FIXED at the collet. Then measure the deflection at the collet, the spindle, the Y axis, the gantry, the gantry sides, and the bed in turn. You will probably see a sudden delta change at some point in this chain, that is where you need to improve things.
For applying force to the collet in X & Y I used kitchen scales (the flat electronic type) with a short length of wood in between to get onto the collet. I was then pushing until the scales read 5kg (~5N). You can also pull with luggage scales for X and Y. For Z I put the scale under the collet and pushed up. I'm not sure how you would do that will luggage scales other than perhaps with a pivot and beam, then scaling the results. As your readings showed the machine is fairly linear so any force (within reason) will do.