base2 

In an earnest attempt to be helpful:
Get yourself a set of Gevenalle shifters $200
Get yourself a shorter "take-off" stem $10
Get yourself a road handlebar (aluminum) $30
Get yourself some bartape, cables & housing $50
Get yourself some decent road tires & tubes $100

At $400 you will have a much, much faster bike than your current configuration. Aerodynamics & rolling resistance mean a lot. The energy conserved on flats will make a meaningful contribution to your reserves on climbs.

The same can be said for your actual hill climbing technique. Sit. Spin or grind (depending on your perspective) at around 80 rpm or so. Hands on the tops, not the hoods. Sit bones a bit forward on the saddle, head up, chest a bit forward, shoulders a bit back, with the roundest pedal circles you can coordinate your legs to make.

Remember to exhale completely so that you can let in lots of fresh Oxygen. It's easy to forget to breathe. I've seen people nearly pass out because they inhaled to "grunt-out" an effort & never let any air out for the duration.

Then as others have said: Group dynamics & strategy for further conservation of energy. The best place to be is right behind the leader. It helps minimize the sling-shot-caterpillar-surge-effect that ejects slower riders off the back & as a secondary benefit buys you a meaningful amount of time on climbs as you fall to the back of the group.

Hills are also about raw athletic capacity, motivation, technique, & determination. You can't buy yourself to the front. You build yourself to the front. Do what you're going to do. Ride what your going to ride. But, you might find it's best to save your light & fancy bike for the group rides. Combine that with fresh legs. Many people "train heavy" & "ride light." It's a time honored tradition.

FWIW: A fancy $4-6,000 carbon wonder bike & no ability would be considered Fredly on the opposite end of the scale. Those guys tend to self-select out of our group before very long. Our group has migrated to "heavy" "gravel" bikes with 38c tires & way too much storage over the years, as the group average over a 25 mile suburb road ride has remained moreorless steady at around 18mph or so. Stay with your current bike.

Make the above changes, build yourself, & do your own work. Kickin' their Aces on what is perceived as "lesser" equipment builds street cred.