I don't know if I can describe this exactly but I know what I would do. I'll give it my best. I am the son of a carpenter and do 95% of all my own home work/maintenance including electrical and plumbing but no HVAC. lol I'll try not to overexplain but not knowing your level of familiarity I'll try to be fairly detailed.
So I would measure the distance from the floor to the bottom of the stand. (I'm picturing something along the lines of 1/4"). Check that this measurement if consistent across the opening. Then measure the distance between the shims. (Something like 69.5") Then I would take a pressure treated 2x4 and cut the total length to match the 'distance between the shims' measurement. Now is the tricky part to describe. The board now needs "ripped" to the proper thickness. Make sure you follow all proper safety information that came with your saw.
With a good circular saw on properly stable platform make sure you have the board clamped down.
Lay the board flat and measure from the edge toward the center of the board. Measure in the same amount as your distance from the 'floor to the bottom of the stand' measurement. Mark one line as close to the mark on the tape measure as you can and note whether the line itself needs to be left or removed to make the board that is being removed the closest fit. You then set the saw on the board and put the blade exactly where you need it to be to either leave or remove the line when you cut. Keep the saw in that position and slide the saw guide into position where it is pressing on the edge of the 2x4. Tighten the saw guide and your thickness is now set. Be sure to now check the depth of the saw. All circular saws should have, usually towards the back, a lever which allows for adjustment of the depth. The depth should be set so that the blade passes just deep enough to cut completely through the wood being cut. You are now ready to cut "rip" the board down it's length.
Once cut you can take your piece in and check for fit. It should be snug and not slide under with no effort. But when you lay it down on the tile you will be able to see if it is sticking way too far up. I also forgot to mention to make sure to measure from the face of the tile and not from a grout line as the completed piece will bridge all the grout lines.
If the piece is snug lightly sand and paint to match your stand then install. If it is too snug you can either try and sand it down to make the fit better or if it is too much to sand then I would reset the saw and cut another piece.
Once you are ready to install I would have just a couple pieces of advice. First I would start the install with the piece up on a 45 angle and push it down and under the stand. Then I would take another piece of wood and wrap it in a towel. I use the towel simply to be a soft cushion against the freshly painted surface I just spent time sanding and painting.
Place the towel wrapped piece of wood against one end of the piece being installed and gently tap the other side of the scrap wood with a hammer. Do this equally from one end to the other and back until it is flush across the face.
Hope you find this info helpful.
