I've now failed two contracts because I was only half way through the "technology" stage whenever the deadline hit. What can I do to complete contracts more quickly?
To complete contracts more quickly, you essentially need to hire programmers that are good at the required discipline (design or technology). The solution is not so much "how to complete contracts more quickly", but more "how can I choose contracts best suited to the attributes of my team".
The amount of design and technology work you can complete is heavily based upon the skillset of your team. For example, I have James Carmack on my team, who is far superior with technology than he is with game design as you can see below;
Meanwhile, my own character is completely evenly skilled across the board;
With this in mind, whenever I take on a contract, I aim for technology heavy contracts. I know that if I go for a contract that requires a lot of design that I will fail it, as one of my programmers is very limited in this aspect.
In the early game, when there is only you working on the project, you are best off aiming for balanced contracts. I failed quite a few early on in this playthrough because I wasn't able to meet the output requirements to fulfil the contract in time. Another thing I noticed, is that if you put your programmer in a position where they've got to do something they're not good at, they will just sit there scratching their head, burning up precious time as your deadline fast approaches.