Cryopreserve at high pressure, and avoid fracturing of tissue (?)
"The form of ice that is created when water is cooled at atmospheric pressure, 'Ice I',has a higher unit volume than the liquid water. As a result, increasing the pressure actually causes ice to melt rather then water to solidify. That is, up to a pressure of about 2000 atm. Above this pressure, other, more dense forms of solid water (Ice II, Ice III, Ice V, Ice VI, and Ice VII) can form." (link)
These ice forms are denser than water. (link) So, perhaps they would not damage the cells like ordinary ice does.
For instance, Ice III is formed by cooling water down to 250 K at 300 MPa (Wikipedia:Ice III). The pressure would occur naturally in the sea, 30 kilometers below the sea level.
"Ice III ... has a density of 1.16 g cm-3 (at 350 MPa where water density = 1.13 g cm-3)." (link about Ice III) So, it's a contraction by only 2.65%, versus the usual expansion by 8.33% upon freezing.
It is very hard to achieve high pressures for macroscopic objects, but it should be very cheap to test this on tiny animals, like, for example, ants, trying to turn them into frozen form simply by pressuring while reducing temperature to approx -23.5'C, so that it enters Ice III directly, skipping Ice I phase. I'm moving this idea here, because I'm thinking of actually trying this out. Contacting labs that have equipment and writing a paper would be a step towards testing this.
The hypohtesis would be that by adjusting pressure and temperature gradually, there can be a path through which we could freeze something like an ant or a bug, and it and bring back to life.
This idea is a bit modified. The original idea was to freeze by pressure alone, because water freezes at +36.5'C under pressure of approx. 1GPa, directly into Ice VI, but this idea was criticized, because the body undergoing such pressure would heat up, and that may cause unwanted chemical changes in the body, even if water stays solid at much higher temperatures with even higher pressures.