Yeah, serving some kind of topspin or no-spin sounds like a good idea, they'll pop the ball up for a smash or flick in a perfect scenario.
Continuing with the serving idea, maybe the placement of your serves enables your opponent to start pushing too easily, try a long serve every now and then, get's the rally moving real quick.
You could also be more efficient or strategic with your short pushes/touches, look at where your opponent doesn't like to receive a backspin ball and force a weak/passive response that you'd be more comfortable attacking. Maybe your opponent likes to push from his BH side, so you send it to the wide FH, make them reach uncomfortably, don't just pass the ball.
You could vary the amount of backspin, force a mistake.
Maybe push long and force your opponent to lift and then counter attack.
Ultimately yeah, you have to get comfortable with lifting backspin when it comes, both safely and aggressively if you can. It takes a bit of getting in the right mindset, so just practice practice practice until it's just your instinctive response, at least that worked for my style.