First off, for permanent use the Diamond is better than the Tram. I have that exact Tram, but I only use it for temporary/weekend projects. If you can afford it use LMR-400 coaxial cable. Alternatively, RG6 may work well enough for the area you want to monitor.
A discone on the roof will help, but it's not that great as it is not specifically tuned for 1090 MHz. Also, if you use a simple T splitter the signal strength will be lower for the scanner and ADS-B receiver. You would want to use an amplified splitter to make up the losses, or one that is able to split the signal, but gives 0 dB gain out so you suffer no loss from the split.
I use an ADS-B outdoor antenna from dpdproductions. It is about 30' above ground and I use 50' of shielded RG6 coaxial cable. I also use an ADS-B filter/amplifier on the coax. Depending on the altitude of the aircraft, 200-250 nautical miles is not a problem as long as terrain (a mountain range) is not in the way. Still, I am more interested in MLAT and share my data with others to plot aircraft. I could use 1/2" Heliax which would keep it at 50 Ohms as well as reduce my signal loss. This would help me a little further out and with distant lower altitude aircraft, but I am not sure I care about monitoring some aircraft at 10k feet 150 miles away. If someone is interested in that area, they should help with a receiver of their own and share the data.
Here's the thing, if you want to just cover the general area where you live, a discone will work well enough if it is above your roofline. Use some LMR-400 coax if you can as it has lower signal loss. What you may not get is coverage of aircraft when they are on the ground if an airport is nearby. Ultimately, I presume the discone is primarily for your scanner. Go ahead and try it on your ADS-B receiver by connecting it directly and not use a splitter. Do this during midday when the air traffic will be busy. If you get the coverage you're looking for, fantastic. You can then purchase a proper splitter and enjoy the discone with both.
Also, have you tried adsbexchange.com? You may not need to worry about it if you're already covered. If you live south of Saginaw that area is covered. If you live north of Saginaw, it needs help.