Yes, RapidWeaver has had some publishing issues over time. But it’s gotten much much better.
… that said I warehouse all images and audio. (All video is via Vimeo or YouTube.) Warehousing has many benefits, but one is certainly that it can avoid RW having to upload a bunch of images several times. I’m paying special attention to what you wrote earlier about Cyberduck also taking a long time and having problems. That indicates the issue is not just with RW.
If I had a 45 page site that is about 20 Mb, and your similar site is 112 Mb, then I’m estimating you have about 90 Mb of images in that project file. That certainly could be the cause of the hiccups. And certainly the cause of slow uploads over time. If you warehouse your images you only need to upload them once! Instead you are essentially uploading your images multiple times (somes as a whole, sometimes as subsets). At the least that will take a long time. For example, I can republish my entire site in less than 5 minutes (max) on a very modestly speeded internet connection.
If you don’t want to slowly transition to warehousing then … you may want to take a deeper look inside your RW project to make sure there aren’t any overly large images, or things like images without proper extensions. To do this be careful. First, duplicate a project file. Move somewhere else on your hard drive. Then right click on the project and select “show package contents”. Now you’ll see the insides of your project. Start looking for your biggest folders within that and checking them. See if all the listed images (they’ll have transformed names from the original) all have proper extensions (.jpg or .png) and check their sizes. This is boring, and will take some time, but if you find just 1 or 2 “bad apples” then it may point to the source of the publication problems. A bad apple could be a 7 Mb image (despite what you think, it’s always possible there’s some “old” image that was overly large from being added a long time ago).