2 things come to my mind: I have used bladders for track-only cars for ~ 20 years old without any fuel-feed problems. Have you checked the fuel filter(s) and the pickup lines? Once I found that issue on a car I had just purchased. The bladder got renewed anyway since I needed FIA approval.
2. Usually the bladder is stuffed into a solid (aluminium or steel) tank - the latter may be part of the body, as on my RCR40. On all my cars I can open this tank one way or another to remove the bladder for service/renewal.