A Hand at the Mirage

Recently I played a hand at the Mirage in Las Vegas that I want to share. I was playing in the $2/$5 no-limit game and had approximately $600 in front of me. Under the gun I was dealt As Kd and raised to $40. The game had been pretty loose and pre-flop raises had ranged anywhere from $25-$50 usually. A very tight player across the table from me called the raise as did the BB who was a calling station. The flop came Qd Jd Td which was a pretty good flop for me but also very dangerous. The calling station led out for $75 from the BB and I decided it was best to just call with my straight and see what the tight player across from me did. The tight player thought for a moment, called time, and then raised it to $225 ($150 more). The calling station disgustedly folded while muttering to himself and that left me with a huge decision. Whenever anyone calls time there is usually big trouble. The raiser only had $75 left in front of him and I had him covered. The raiser was obviously going to put in his last $75 unless it was a complete bluff so I was going to have to invest another $225 if I wanted any chance of winning the pot. If we both got our money in there would be $800 in the pot ($40 preflop + $40 preflop + $40 proflop + $5 SB + $75 on the flop + $75 on the flop + $225 on the flop + $75 the raiser's remaining chips + $225 I would have to invest to stay in the hand). So I had to put $225 into a $800 pot. I'd need an expected value of at least 28% to stay in the hand. Most people at the table thought I should fold the hand since the player was very tight and unlikely to raise without a flush. I approached the hand from a slightly different angle though. The player across from me was very tight. So, what hands could he be calling me with preflop that would give him a flush? The Kd was in my hand and the Qd, Jd, and Td were on the board. For him to have the nut flush he would have to have Ad xd. This guy seemed too tight to be calling $40 raises with Ad xd. 9d 8d was a possibility also but I had put this guy on a bigger hand. The hand that came to my head was Ad with a K offsuit. With that hand he knew I couldn't have the nut flush because he held the Ad and he knew I was a solid player who raised under the gun. He knew I wouldn't raise UTG with Kd xd. Now that I put him on Ad Ko what do I do? The best I could do is split the pot unless I caught my miracle 9d. I quickly figured that he had 7 outs to win the hand, while I had 1 out to win the hand. 7 outs twice is approximately 28%. I figured 28% of the time I'd win nothing. About 68% of the time I'd win $400 (half the pot) and 4% of the time I'd win $800. Without doing the math I knew the expected value was much more than what I needed to call (It's actually $304 when I only have to put in $225). I then pushed him all-in for his last $75 because I figured that money was going to get in the middle anyways. He actually laughed at me as he flipped up Ad 2d. My read was dead wrong! I was dead to one out. For me the story ends happily as the turn brought the beautiful 9d. Ship it! The other player kicked a chair on his way out of the poker room saying that the game must be rigged. I really did feel a little sorry for him but not enough to give him his money back. I mean who calls my raise with Ad 2d? Just kidding. Some would say the lesson is not to overthink the hand (I mean the guy did raise into a very dangerous board after calling 'Time') but I'm happy with my decisions. What do you think?