Is there any good reason to keep the higher liability limit on the
homeowners policy, or should I lower it to $300,000, since the
umbrella policy will take effect after that?
The umbrella policy is on top of your other insurance, so lowering the homeowner policy liability limit by $200k decreases your total coverage by $200k.
Common guidance is to have an umbrella policy that covers your net worth, if your umbrella policy already exceeds your net worth then dropping some liability on the homeowner policy could save you money. If you feel that you need that $200k in coverage then it's more a question of which policy gives you that extra coverage for less premium (not always apples to apples as what gets covered can vary).
Personally, I have the minimum liability required by my umbrella policy for my homeowner policy because that's how my insurer writes those policies together. I'm not sure what factors get utilized in pricing an umbrella policy with a separate insurer, but if you had to provide your other coverage details when applying for the umbrella policy I could see a potential for it to impact your umbrella premium if you reduce other coverages.