Memorial service open to public followed by more private gathering

Yes absolutely no gathering now!! Covid restrictions are the reason behind the delay of the memorial service just as Oopsadaisy mentioned.

The OP wants to have a Memorial Service ‘when it is safe’.

It's illegal to organise a gathering right now. Why not adapt to the present situation, abandon traditions - and stick to the rules - please!

Zoom has been used for the funerals I know of in recent months

Is this in a Covid free country?

At my father’s memorial service and internment in the family plot, sometime after his cremation, the church was packed. Only family were invited to the internment in the churchyard.
I don’t think any of congregation expected to be invited to the repast.

Just write ‘family only’ for that part of the service. I have come across this a number of times. You can ‘word up’ close friends that they can come, too. It is quite normal for this to happen here.

I didn’t want to just read and run. But it’s a tricky one isn’t it?
A lot of people will want to go and have a drink with the family after a Memorial Service, whether they know them or not ( not being unkind, but where there is likely to be free food, there will be people) and it’s trying to keep them away that will be the problem.
Unless you go and have the food and drink later in the day, Memorial service at 10 am, then meet up with family and friends, by invite only, to afternoon tea at 4pm.
I think if the attendees at the Memorial service see everyone drifting away to their cars with no mention of food and drink, they will assume that they need to go home too or take themselves off in groups themselves to toast the deceased, otherwise they are likely to just follow you.