I dont think the adding menu view to app is not going to give an visible impact to the sync speed, but it is minimal.
What is making you difficult to add this menu view to each app? I actually have same use cases, to place the same menu view to a group of apps.
Yes, it is hard to add the same view each time, it is time consuming, but we do once, then no more concern.
What I do is make one spreadsheet just for menu.
Then for images and icon, I host images somewhere else, not within Appsheet. On the above mentioned speadsheet for menu, I place URL to reach out to such icon image with full URL.
From each app, I read this table. and make a gallery view.
Each app is refering to the same spreadsheet, and maintenance is easy. Just update spreadsheet and this change will be reflected to all the apps.
Adding full path url to the images will eliminate the works to add images to each app.