This answer to the question Is Io a magic energy machine? suggests that the energy from the internal heating of Io due to tidal "squishing" as it moves cyclically closer and farther from Jupiter in its elliptical orbit will come from the energy of Io's orbit. A lower energy orbit is necessarily smaller, and that actually means that the velocity will be larger. (When you want to raise a satellite's orbit to a higher altitude, you actually use thrust in the direction of motion to slow it down.)
Given that tidal forces are a little complicated (cf. Why is the Moon receding from the Earth due to tides? Is this typical for other moons?), is it a priori certain that the heating will lower Io's orbit, causing it to speed up? (Consider that Earth's Moon's receding is due in part to Earth's liquid ocean, and Jupiter is a gas giant.) Is it just the perijove that will decrease, or the semi-major axis?
How can a (seemingly, naively, on average) radial force cause a tangential acceleration? Io is tidally locked to Jupiter so its rotation around its own axis is synchronous to its rotation around Jupiter.
edit: fwiw if the gravitational interactions between Io and Jupiter's other moons causes the problem to be too complex to answer easily, I'm more interested in the basic dynamics of tidal heating and effects on the orbit of a single moon, rather than specifically Io's situation.