Thanks for your response, RW. Aluminized mylar seems to be an optically thin aluminum layer with polymer on both sides. Do those divots mash through all three layers and make contact with the aluminum layer in passing?

They might just stretch and thin the polymer layers until quantum mechanical tunneling occurs between aluminum layers. In that case, a set-screw fitted to a little brass clip might give more reproducible results.

Also, I am not after secrecy levels of RF attenuation here, just health protective levels, which should be easier to achieve.

There's a fugly but kinda works and good enough for stuff I've done, method.... aluminum tape... then punch divots in it with a rounded tip, like a pen will work, just to mash things together but not really penetrate. Then also you can kind of knurl the edges down like it's some kind of pie crust by hashing it with a blunt knife, again the object being the mash the metals into each other without penetrating. You kinda get a half rivet, half microweld thing going on, but not all of them are gonna contact well so you need to do lots. It's been good enough for my purposes, but I've only been grounding half a dozen watts and not running millimeter wave stuff where a small divot will diffract or anything strange. There's another option... tape it together with any durable tape, close an edge fit as possible.... needs a decent coating on the substrate though, or this prep step... wipe down with oven cleaner or dilute sodium hydroxide solution... will take it off... then copper plate the join with copper sulphate solution. If it's thick stuff leaving quite a valley, or the edges are a tad rough, you maybe need to rub graphite up and down it. I have managed to plate on aluminum immediately after mechanical or NaOH cleaning. Some trial and error may be required. So if it's a one-off material acquisition then maybe forget you read this :-D 

that's a hard problem to solve.  Matt Blaze did a study of DIY Faraday cages here https://www.mattblaze.org/blog/faraday/ that might be an interesting read.

Thank you. The reference shows that it’s possible but not straightforward. So somebody’s patented the method by now and I had better look at the patents.

How do I make a hollow tube out of aluminized mylar sheeting? Will the seam be problematic?

if you need flexibility or the ease of manipulation of a physical connection you will need to use a wave guide. Essentially a hollow tube.