I dont think cycling at your level is at odds with strength training and having a ‘beach bod’. Body builders recommend the walking and only doing cardio for a cut phase leading into competition. But for normal people, you can improve both aerobic fitness and physical strength / muscle simultaneously as long as youre getting enough nutrition. Literally, just make sure you are getting enough nutrition and enough recovery and you can train however you want.
For example, look at elite rowers (aerobic athletes)… They are all ‘beach body’ aerobic athletes. Most elite cyclists are thin because they purposefully push their upper body weight downwards to increase w/kg ratio (and that upper body muscle mass is not very beneficial to performance).
When I lift, I combine it with a hard cycling day (cycling workout first, then lift) or I do it the day after a hard cycling day. I do this because I care more about optimal performance for cycling, and by combining them I can go hard then recover rather than always be slogging away (insufficient recovery - living in the ‘grey zone’). You might want to try that