Since you've chosen not to purchase the specifically designed edge pieces, you've limited yourself on options. I see two:
- Epoxy the decking to the wood.
- No visible screws
- Can also be used to attach the fascia board
- Doesn't allow for expansion of wood
- Reasonably permanent with no simple way to remove the board for future repairs
- Screw through the edge groove roughly following the green line in this image:
- Reasonably quick and simple
- Grey decking screws with small "finish" heads are available
- Allows for easy removal in the future if necessary
- Allows for expansion in the wood with minimal worry
- Uses screws (not an option based on the original question criteria)
- Most likely will require pilot holes for each screw
- Leaves the tongue showing on the edge board, but you've already decided to live with that.
- Might interfere with the fascia board below it, but you can cut off part of the tongue of that board to make clearance
A follow up thought occurred to me that would allow attaching the fascia board, as well. If you flip the fascia board over so the groove is facing down, you could screw the last deck board down through the groove, but at a steeper angle, as shown by the yellow line:
Then screw up through the groove in the bottom of the fascia (following the red line) to hold the bottom of the fascia in place. Obviously, you can't have the red & yellow screws lined up vertically or you risk them hitting each other, but offsetting them is a challenge most people will overcome naturally. ;)
- Provides an attachment method for both the deck boards and the fascia boards
- One screw will hold down the deck board and the top of the fascia
- Requires a fairly long screw to hold down the deck board, go through the fascia board and into the rim joist behind it
- It may be difficult to get access to drive a screw up into the bottom of the fascia board
It probably isn't necessary to go nearly as vertical as the yellow line depicts, but just steep enough to get a good purchase on the fascia board. This should suffice to give you the idea without me having to provide a specific angle. You may consider doing a couple of mock-ups similar to what you're holding in your hand to determine a good angle.
You've backed yourself into a bit of a corner (IMHO) by choosing not to go with the edge solution provided by the manufacturer, so you may have to make some compromises on look, materials and methods.