you can do everything you want with Crestron but it won't be cheap and you'll need to learn Crestron programming. The way I would handle this is to break down what you're trying to accomplish into it's component parts, first you need to determine what you want to do
Goal:
1. individual sources per TV: to me this means you do not want to be able to view the same source on different TV's, for example, your ps4 will only play on one TV and always the same TV.
2. Individual control of each TV and its sources.
2. Use 1 DVD player for all sources.
Hardware:
1. You will need 1 HDMI switch per TV, the number of inputs depending on how many devices you want to feed to your TV, here's a cheap 5x1 switch, 5 sources to 1 TV (
http://www.monoprice.com/Product?c_id=101&cp_id=10110&cs_id=1011002&p_id=8203&seq=1&format=2)
2. You will need 1 pair of cat6 runs per TV for HDMI over cat6, there are baluns that will do this over 1 cat 6, I prefer to use the dual cat6 solutions. I wouldn't use conventional hdmi cables for anything longer than 20 feet straight run.
3. I would also run 1 cat6 for each TV in case you have smart tvs and they require internet, I prefer not to use wifi if I don't have to.
4. Run 1 cat6 for remote infrared, in case it's required by the blaster you choose, some blasters will work on a network, for others you can use the cat6 to send the IR signal to a remote blaster.
5. Your issue will be the DVD player, splitting a digital signal to be viewed by multiple devices at once can be tricky and may require a scaler at each destination device (or at the hdmi switch controlling each device). In the simplest terms, you will run a pair of cat6 for hdmi from the DVD to the basement. In the basement you will split the output from the DVD player into 6 outputs using an HDMI splitter, 1 output going to an input on the hdmi switch for each of the TVs in your house. That means whatever is playing on the DVD can be seen by all the TVs in the house should the TV's hdmi switch be set to that input. If all your TVs are identical, you may not have scaling issues. Here is a cheap hdmi splitter
http://www.monoprice.com/Product?c_id=101&cp_id=10113&cs_id=1011308&p_id=8205&seq=1&format=2
Control:
1. Everything you're asking for can be controller through IR, I've never used RoomieRemote but from looking at it, it should do everything you need.
2. My only concern is that the blaster should work on a device specific manner, not line of sight. In other words, you don't want the blaster to send the commands to every device in the basement, just the devices it needs to control. You can accomplish this by segregating the devices for each room, so that the blaster signal from 1 room does not bleed into the devices for another room.
3. Normally, I would get 1 blaster, with individual outs and connect 1 output over the IR received of each device. You'd have to see how roomie handles that.
I'm not an expert and I'm sure there are tons of things I'm forgetting to leave out, but maybe the community can help build upon it and/or correct me where I'm wrong. If you want to go with better equipment, check out Atlona or snapav.