Interesting. I never really considered the Inspire 1 a "lifter." This derived from my experience with the Inspire 1 regarding camera packages. Going off memory, I believe the X3 weighs about 250 grams and the X5 weighs in around 600 grams. That mere 350 gram difference REALLY changes the way the Inspire 1 handles. I never flew with the X5R, but I could imagine that that payload is probably 750 or 800 grams. I can only imagine how poorly the I1 handles with that package. Worth noting, all my experience is in the 5,000 - 7500 elevation range. So if you're at sea level, you may see better numbers and handling characteristics. That said...
Your FPV package sans battery probably weighs < 150 grams. Add a SMALL battery and I'm sure that takes you close to 200g. I honestly don't think I would feel comfortable with a total payload of any more than a Kg. Even then, as you stated, flight time will be highly compromised. As if that weren't bad enough, new Inspire 1 batteries are nearly impossible to find. I have about a dozen Inspire 1 batteries and I can tell you from great experience that flight times start to wane around 50 flights. The loss is gradual so I have batteries with over 80 flights still in service. I am **** about battery maintenance and storage. By my estimate, with a 1 KG payload and a newish battery (< 40 flights), assuming minimal battery draw from the sprayer, I would estimate flight times to be dismal - somewhere in the 7 minute range.
I don't want to discourage your project, but I my objective is to help keep your expectations reasonable.
If you deliver real numbers (weights, elevation, current draw, number of flights on your batteries, etc.), we can better calculate what your real-world flight times might be. But honestly, I bet my "educated guess" is not more than 10% off.
Oh...almost forgot... I would install the payload under the fuselage.
D