A blender can quickly infuse something like this into vodka, you might try making a little cucumber vodka instead of trying to get the flavor into the syrup? I've used it with ginger and also celery. Blend then strain.

I found some success simply mixing cucumber juice with simple syrup, sort of like a cucumber aqua fresca, but it wasn't as... cucumbery as I wanted. It worked well enough for a cucumber gin fizz, but I think there must be a better way to extract cucumber flavor for bright refreshing punchy cucumber drinks.

The cucumber watermelon aqua fresca I made worked like a charm and did brilliantly in a tepache and tequila cocktail I made with it. Maybe cucumber is naturally mild and the deficiencies in the flavor were hidden by the presence of watermelon.

As required by law: a cocktail. Lime, darker cuke syrup, gin. Tastes fine even though it looks like brussel sprouts.

I would just be chucking fresh cut cucumber into the tin I'm using or muddling with ingredients in a vessel before adding ice and stirring. Make an eastside like this and compare with eastsides made with your syrups instead and let me know how it is.

2 gin, 1 simple, 1 lime + cut cucumber as desired shaken and strained for quick reference.