A custom trip may or may not be possible, but it would mean the two of you would have to pay the whole ship, which is meant for cca 15 people, so it would be costly.
The trip I did covered the dragons on both Komodo and Rinca, Pink Beach and Gili Lawadarat (perfect view definitely comparable to Padar without any crowd). If you insist on Padar, I guess you would need to go for it from Labuan bajo as a day trip together with Komodo and Rinca (maybe day trips to Padar only are also possible). The advantage of sleeping on the boat in Komodo archipelago is that you will be at the view at 7 am, while leaving from Labuan bajo for a day trip, you would make only several hours later.
