I think the point of stealing holy relics is to take them to your own homeland and erect a shrine for them there so as to attract pilgrims. Rather than to exchange them for some finite sum of money.
What I was thinking of was that the Rhomaioi Emperor agrees to give the Venetians some Eastern Imperial backing and support in the war on the provision that they are handed back the remains of St. Thomas from the heretical Apostolics of Espanea, which the Venetians agree to. The Doge receives a large sum of gold from the Emperor, and a smaller fleet, and off they go to fight the Espaneans. Then they suddenly find themselves with the bones and... did the Emperor say he wanted this to go back to Edessa? I wonder how much he really, really wants that...
The Venetians takes the relics back home, and there is a huge diplomatic mess as to who deserves ownership of the relics. The Venetians never planned to keep them, but now that they actually have the body of a disciple of Jesus Christ himself they find themselves oddly reluctant. The Emperor, to avoid embarrassment of having the body end up in the hands of another power, now has to agree to pay a ridiculous sum just to get it back that wasn't part of the original deal. This seriously damages the already declining Byzantine-Venetian relations.
After a siege of Edessa by the Venetians, a sack takes place as the besieging soldiers let loose their rage on the city's inhabitants. In the confusion, a company of mercenaries breaks into the church where Saint Thomas is stored, and snatch the saint for their own selfish purposes. Some high-rolling merchant from some place like Tyre or Alexandria may have persuaded the captain of the company covertly to recover the relics in return for a substantial reward. Afterwards, the Venetian colonial would take the relics to his own church. From there, jealous rivals from all over the place would try to use whatever means to snatch the body of Saint Thomas. Until years later one group from the enclaves in India eventually acquires the body.
That seems like a perfect way to have them finally come to India. Can we allow both scenarios to happen, mine first, ending with the bones coming back to Edessa and then yours, retelling how they find their way to India? That way the body of St. Thomas gets to travel around a little on the Med.