People can say what they want to about the LCD Dipstick being a POS, etc, but this is precisely why I like it. Not because it is the most accurate regarding temperature readout, but simply because it's an easy way to check the oil level when hot. And I have not personally experienced any issues with the LCD stick after 25K+ on one bike and 6K on another. If I've just done a 150 mile run down the Interstate at 75-80mph, pull into a gas station to empty one thing and fill up the other, it gives me some peace of mind to push the button to make sure all is well. I'll still do the occasional cold check in the basement before a ride too, but hot checking the oil with a dipstick is a PITA.
How long since you had the bike serviced? Do you know for sure that it was full of oil after the service? If so, how many miles since? If you had it serviced, know that it was full, and it's used 2 quarts since, you have an issue. Whether I would be concerned about mixing the Dino oil with the "synthetic"...not so much if I only had 1K left until the next service, but if I had 4K left, I'd likely change it just for my own peace of mind. As Jerry (grc) stated, if for no other reason than the fact that the synthetic is able to handle higher temps, and it's summer time.
Damage to the engine? That's hard to say. If it's been 2 quarts low for 2K miles, I might be concerned, but if it's relatively recent, not so much. It sure isn't a good thing to run it 2 quarts low for very long, IMO.