Question in the title, can Davith use force speed while occupying another figure's space, ie while spending movement points but before ending his movement. The RRG just says abilities like Davith's (use during your activation) can't be used while resolving an action, but spending MP isn't an action.

Force Speed: 1[strain]: Use during your activation to move up to 2 spaces. Limit once per activation.

Movement Points: Spending movement points is not an action and may be done at any time during the figure’s activation. They can be spent before or after performing any action but cannot be spent while resolving an action.

Abilities: An ability that can be used “during your activation” can be used before or after performing an action during an activation. It cannot be used while resolving an action.

Abilities that are not actions can be used while sharing a space with another figure. These include Force Speed, Force Throw, and Battle Technician to name a few.

However, rules as written do not allow you to enter a space with another figure if it would use up all of the movement points, apparently trying to convey that you would need to be able to get to a valid space afterwards to end movement. Whether to allow Force Speed to fulfill that requirement (instead of saving 1 movement point to be spent after Force Speed) or not needs a ruling or agreement.