The only way the 30-day trial stacks with a full PS+ sub is if you use the trial first. You can apply your 1-year sub at any time.
I don't use my credit card either, but that's so I don't increase its balance - either I only buy stuff with (PayPal) cash now.
Even if adding a trial code requires a CC, you can delete the card's info from your SEN account as soon as you use it for its single purpose.
I added 30 days to my existing Plus account using the trial that came with my PS4, so they will stack no matter what order.