This might be fairly obvious - and restricting, which is why others may not want to endorse it - but the best way to develop musical ideas without feeling like you're forcing it is to only work on music when inspiration strikes.
This is probably a no-go if you work in the music industry, but if all you are is a music hobbyist (like me), such a schedule is often fine to stick to and maintain.
I must admit that I still tend to force it somewhat often, including when composing for contests and composing inner sections of classical music. Probably like you, my favourite compositions of mine tend to be non-contest entries (or compositions made for very lenient contests such as "anything newer than this post that is 4 minutes long or less is accepted, due date is a month from this post") - most of my contest entries had to follow fairly restrictive rules that I often felt like I had to force music through and use several of my worse musical ideas for.
I have several musical works in progress on my computer, some of which have not been updated in years, and several of my compositions involve a musical form (sometimes considerably detailed) chosen in advance where inspiration for any of its musical themes did not come until several weeks after I chose the form. I even have lengthy melodies (20 seconds or longer each) of my very incomplete Symphony No. 1 in G Minor stored only in my mind and emitted on occasion when I sing them to myself alone. All of these ended up this way because of my basic tendency to only work on music, especially those works, when I get the inspiration to work on them further.
There is a considerable cost to only composing when inspiration strikes, but if you want to feel the best about all your completed music, it might still be worth the cost.