If you check the old Index Astartes article on the Deathwatch, they were functionally identical to Sternguard anyway. Sternguard were almost certainly designed using the ideas from the slush-pile for the cancelled Ordo Xenos codex.
Play Sternguard; paint them as Deathwatch. Make a Deathwatch allied contingent (convert a tactical squad for the Troops). Or just ask your friend if you can play your lovingly converted and customised kill-team in a game. Or do what my friend does and only ever play Kill-Team. With your Deathwatch. There's your Deathwatch. Enjoy playing your Deathwatch.