Sigma 150-600 definitely looks like a fantastic lens, but it's a good £2-300 out of budget, plus it's 2kg, the wife complains about the kit lens being heavy and it's .45kg! lol. I figure the Tamron 100-400mm is a good in-between at 1.1kg and is basically up to 640mm with the canon crop sensor?
You are asking the wrong set of people - they are really into their photography so don't mind lugging around tons of kit. I do the same when I go to airshows,etc. So monopods,tripods,etc. I also have a lighter mirrorless setup with a lighter telephoto lens when I go on holiday,and it avoids me needing a camera bag to carry my other setup.
Regarding the focal lengths,more is nicer,but plenty of people use 400~500MM lenses on even 35mm frame bodies to good effect. So I think a 400MM is not necessarily a bad idea.
Remember your camera is quite old now,it only has a 9 point AF,and a small pentamirror viewfinder which probably doesn't help - a camera with a larger pentaprism or electronic viewfinder is really helpful(especially in terms of brightness). Also as the 500D isn't the biggest camera,a huge lens on the front of it will make it lopsided and very front loaded. There is a reason why the professional bodies are chunkier,and you need to be wary of the weight on the mount too.
Although I am surprised no one has suggested a decent camera strap. Something like this will help a lot:
https://www.amazon.co.uk/OP-TECH-1501012-Pro-Strap/dp/B00092KD9C
It actually distributes the weight better over your neck and shoulders,and it won't cut into them like many of the included straps.
If you wife,really does not want a heavy setup,then you are throwing money away getting some of these recommendations,as your photos are going to be only as good as the lenses you bother to take with you. Also if you want to take quick pictures,a heavier more unwieldy setup is not exactly helpful!!
You will also need to invest in a bag too,to carry around the lens and monopod if you ever want to use it on holiday,etc.
Think if from that perspective - how much use is the lens going to have,especially if you want to travel. Honestly,I would get the lighter setup.
I would also actually try and find a good camera shop, and try these lenses with your camera,to see which ones your wife thinks she can tolerate.