Hi, Just curious how to go about this without breaking the bank. I’m guessing an 11-34 cassette is one option, but not much of an improvement for really steep climbs. Sun race offers an 11-40 8 speed cassette. Go Road Link? Mtb rear derailleur (Shimano 9 speed has same pull ratio?).
Two thoughts. I use 11-40 with an 11 speed group set for mixed riding (46/32 front). I do a lot of steep climbs so, on balance I don't mind that the jumps are large. But I would if I only had 8 cogs. This would increase the worst of the jumps from 15% to 20% or more. The other thought is about capacity (the difference in front chainrings plus the difference in high to low cogs). A quick look and your capacity is likely 37T which is how you are set up now. 2T overcapacity is going to be ok. An 11-40 would put you at 8T and this would not be. A roadlink doesn't fix that problem - it only helps the derailleur reach a bigger cog. So, a 6% improvement is not a lot but if the 11-34 is a $20 DIY it's well worth it.