Challenging research design and trouble with data entry and analysis in SPSS

Dear all,
I have been given some data to analyze with SPSS but I am stuck and would like some help.

The design is the following:
There are 40 participants in total, two types of computer devices (desktop, mobile) and two types of software for drawing sketches (soft1, soft2). Participants were asked to perform 7 drawing tasks and objective (e.g. time for task completion) and subjective measures were collected (e.g. usage satisfaction rating). All participants did 2 consecutive trials randomly assigned in the following sequences:
  • 20 subjects used first Soft1 + desktop and then Soft2 + mobile
  • the other 20 subjects used first Soft2 + desktop and then Soft1 + mobile

I have created composite scores from the 7 tasks, so I now have 3 dependent measures (% task success, task time, and 1-10 satisfaction rating) and want to investigate:
  1. if the device type has an effect on the 3 dependent measures
  2. if the software type has an effect on the 3 dependent measures
  3. if the interaction device type * software type has an effect on the 3 dependent measures

Some thoughts:
  1. Clearly, not all participants received all possible combinations (i.e. soft1+dektop, soft2+mobile, soft1+mobile, soft2+dektop), so it is not a typical repeated measures MANOVA design. My first attempt was to use two dummy variables (Device and Software) with 2 levels each, and one variable for each dependent (resulting in 80 cases since each subject has two trials). In this way it seems that I have two within-subject factors (i.e. Device, Software) since all participants used both devices (if we ignore soft type) and types of software (if we ignore device type) and their combination Device+Software forms a between-groups factor with 4 levels and 20 people in each group (but can we have a composite factor? and if yes how can one define it in SPSS?).
  2. I also did some research and I bumped into the “Crossover study” design, so I think that I might have to use some type of Mixed Model (haven’t used it before), but all the examples I have found had one within-subjects variable and I am still stuck at how to enter the data in SPSS.

Any insight and/or suggested good readings for this case will be greatly appreciated. Thanks in advance.