I've been fascinated with geodesic domes since the seventies (last century) and had given some thought to the problem you face. Unfortunately, there is no single-sheet solution to this puzzle.
You may have noted that a geodesic sphere from which the dome is built is constructed of pentagons. You can determine the frequency of a dome by counting from the center of one pentagon to the next the number of struts.
As such, one can cut a sheet of plastic to match the individual pentagons, but it still means that you have to slice a single segment in order to either tape flush (butted) or overlap on the pentagon each sheet. You can get reasonably tight coverage in this manner, but one may consider the taped joints to be unsightly.
The remaining segments that are not pentagons have to be attacked individually. Your selection of a 3v dome gives you a bit of an advantage in that the remaining segments are hexagons, with a center point, with radial struts of the same length, which can be approached in the manner of the pentagon.
Some geodesic designs use individual triangles for construction, which results in duplicated struts at every connection, effectively doubling the material along each path between vertices. This would allow you to pull the plastic into the joint rather than to have to tape or otherwise fasten the plastic to the outside. Think picnic tablecloths draped over the edges, while butting another table against it.
In the case of your EMT based product, this is impractical, especially as it doubles the cost of materials.
You could create an add-on solution by attaching furring strips or similar panels to outline the pentagons and hexagons, using them as clamps to secure the plastic to the EMT. It would still be necessary to slice one sheet per pentagon and hexagon to pull the perimeter tight and secure with the clamping system.
I would hesitate to drill that many holes through what is relatively flimsy EMT and instead would create a hot dog bun or I-beam type of attachment, which would allow for the bolts securing the wood to the EMT to pass alongside the EMT rather than through it.
You could pass the plastic sheet between the top wood block and the EMT or perhaps staple the plastic to the outside of the wood block or to the edges of the block, leaving the top surface of the wood exposed/painted/treated.
One characteristic I recall from my years of reading of construction and pondering geodesic domes is that homespun solutions always had leaking problems!
Silicone caulk/sealer may be desirable to provide additional leak protection.