The Rubrics of the LOTH require that the verity of the hour be respected. That is, morning prayer should be in the morning at or after sunup, daytime prayer at one of the three minor hours or thereabouts (mid-morning, noon and mid-afternoon) and Vespers in the evening.
The Office of Readings has flexibility.
Since you’re not bound to the Office, I would say “do the best you can”. To my mind, the Office of Readings is the ideal Office for you as it can be said at any time, plus it has such a rich treasury of biblical, patristic and hagiographical readings. In religious communities, it is often anticipated the previous evening.
Looking at your schedule, I am guessing that you go to bed at 5 am and rise at 1 pm. You can therefore pray mid-day prayer, Vespers and the Office of Readings at their appropriate times. Lauds can theoretically be prayed at 5 am, especially in summer when the sun is coming up that is an appropriate time. Often in monasteries it was prayed just after Vigils (Office of Readings) and Vigils was often at 2 to 5 am depending on the community (even earlier among the Carthusians).
Compline is trickier. I would ask: do you have a rest break during your shift? If so, I would think that a reasonable schedule would be something like:
5 am: Lauds (Morning Prayer)
1 pm or just after: Sext (Mid-day prayer, and as a Carmelite said on a recent newspaper interview, “be sure to NOT leave out the T when you print the article”; who said the religious don’t have a sense of humour?)
Around supper time: Vespers
Before leaving for work: Office of Readings
At your mid-shift rest break: Compline (night prayer); if you aren’t going to bed, then your prayer is always associated with the prayer of those who are resting. Remember, the LOTH is not strictly speaking a prayer for ourselves, but for the entire Church!
The Rubrics of the LOTH also allow combining Offices, especially the Office of Readings. So that is a possibility; most often it is combined with Lauds, Vespers or Compline. I imagine though, when you come home at 5 am, you aren’t too keen on a very long Office.
The beauty of the LOTH is its flexibility. The example given above is just one idea, you can play around with them. Remember that the “verity” of the hour doesn’t mean an exact timetable. Morning, mid-morning, mid-day, mid-afternoon, evening and night are all flexible concepts. For example I pray Sext at noon, but on Sundays I don’t get home from Mass until around 1 pm, so I typically pray it just after I get home.