Generally yes, handling the important logic on the server should fix your gameplay problems.
About the replication delay, it’s not that bad after all - as I tried to explain above, the whole game has this delay.
The light of the sun takes approximately 8 minutes to replicate from the sun to the earth. Do you ever notice the delay? Our nerves ain’t transfer data instantly either, we all live in the past.
Though game networking is of course a little different and you have variables like the Players ping etc. You may want to read up how the different AAA titles handle delay compensation. Unfortunately I don’t have any Epic related articles to link, so I’d just suggest to search the web for it.