repeated measures, 3 conditions and multiple DV's in each of the conditions

Our experiment design is kind of complex:

35 participants, stimuli were approaching cones that disappeared at different distances (conditions: near (20 cm), mid (60 cm) and far (120 cm). The cones were seen through the oculus rift. Participants estimated the distance where the cones disappeared by moving a square in the distance in the virtual environment. The perceived threat for the three conditions was measured on a 7point-Likert scale. Moreover, participants received a motor vibration cue on the cheeks and were instructed to press a button after the cue onset as fast as possible. The cue onset also had 2 conditions: when the disappeared cone traveled to the observer and hits the cheek (fixed cue) or it could be random (random cue).
We also have scores for a STAI questionnaire: A score for Trait anxiety and State anxiety. Each individual participated in all conditions and the score for each variable in the three conditions is the average of multiple measures.

So we have 1 IV with three levels (near, mid, far) and 3 DV’s:
Distance Estimation, Threat and Response time (with 2 additional levels: fixed/random) all measured multiple times for each individual in all three distance conditions near, mid far.

The data for each participant is the average of multiple measures and looks like:
Estimation in cm: Distance_Estimation_Near, Distance_Estimation_Mid, Distance_Estimation_Far.
Perceived threat 0-7: Threat_Near, Threat_Mid, Threat_Far
Response speed in ms: RS_Near_Fixed, RS_Mid_Fixed, RS_Far_Fixed and also RS_Near_Random, RS_Mid_Random and RS_Far_Random.
We also have a state and trait anxiety score with a max score of 80 for both.

Our research is aimed to find out whether cones in the peripersonal space would be more threatening and more underestimated in distance, and if there are more estimation errors with high threat in the conditions. Furthermore, we wanted to find out if underestimation might be adaptive for a fast reaction, so we want to find out if response speed is also faster/slower for the distance estimation errors at different distance conditions (near/mid/far). Moreover, we included state and trait anxiety to find out of this had any influence on the estimation, threat and response speed. High state anxiety was thought to increase the distance underestimation, threat and a faster response speed in the peripersonal space condition.

What analysis is possible or the most appropriate to test the effects in this dataset?

We tried repeated measures ANOVA’s on distance estimation(3), threat(3) and response speed(3x2). But we also want to test the interactions and effects of threat on distance estimation etc.

Any advice is appreciated! :)