Like the others, I'd say if you have the time, physical energy and the enthusiasm to do it now, go to India! Canada is right across the border and not going away anywhere
Your $10K budget should be plenty for a very comfortable India trip for two, and unlike what Slumdog Millionaire and the likes would tell you, Indian cities and trains today are pretty modern and welcoming to a foreign tourist.
Like jis said, with a good deal on flights, your roundtrip tickets for two will come to about $3K, max $4K if you are inflexible with airlines and dates. That leaves you $6K USD = 360,000 Indian rupees which is aplenty.
If you stick to the highest class of service on trains- First AC on Rajdhani and Duronto class trains, each ticket for an overnight or longer journey will be about Rs 5,000 including meals. One word of advice- First AC is very comfortable and safe, but IMO very sterile since the occupants are either government employees using "free" passes or very wealthy businessmen etc. If you really want to get a taste of India without getting yourself too dirty, do some of your journeys in 2A, 3A or even the non-AC Sleeper class if your wife is okay with "roughing it out" a bit. That is where you will get to experience the *real* India, and some very interesting conversations. Just stay away from the "unreserved 2nd class" for the love of all that is holy!
Regarding safety, of yourself and your wife- Observe regular heightened awareness of surroundings and don't get freaked out and you will be fine. Yes, as a white (or even black) foreign tourist, you will get a lot of glances and stares from the locals outside of touristy areas, but 99.99% times they are harmless curiosity since those people may have never seen a white man and woman all their life. Indian train travelers tend to be very social in general, they may ask you all sorts of questions, including what we consider here too personal like where do you work, or even how much do you earn
but if you can take it in your stride (answer anything random, nobody is going to cross-verify, you can say you are the next Bill Gates if you want to) you will find the co-passengers become very friendly and will offer you food/drinks etc.
Send me a message if you need any help making an itinerary etc. I have traveled about 50,000 km on Indian trains over many years (though very little lately).