There are three fundamental ways to improve your intonation, practise, practise, practise. Having said that, you must practise correctly. A dear friend of mine and screech trumpeter of the Daly Wilson Big Band (during the 1960s), Norm Harris, always said to me: ‘Practise doesn’t make perfect, perfect practise makes perfect.’
With this concept in mind, make sure: a) you have an excellent teacher; b) always work on, or find ways to constantly develop your aural acuity (this, I believe, is THE most important quality of a performing musician outside the actual physicality of performing) and understand how intonation ‘works’ (hence me writing my book, Understanding Intonation for Musicians (not Mathematicians).
In reading your question, many of the answers you seek can be given by a good trumpet teacher or coach. From my perspective, if you sound like you’re getting flatter as you ‘go up’ then you’re probably getting flatter. So, find ways not to go flat. A good trumpet/cornet player will coach you how best to do this. My ‘expertise’ is more along the lines of how a particular note sits within a chord and how, in some instances, you have to play a note very, very flat to be in tune. Go figure!
There are, in my opinion, three levels of intonation to be considered:
Level 1: learning to play a note straight and in tune with ‘something’. The best ‘something’ is a good chromatic electronic tuner (a good stand by is a well tuned piano) that can give a steady sounding note for you to ascertain your pitch (you need good aural acuity to ascertain your pitch…so do everything you can to develop it).
Level 2: Once you have learned to play a note reasonably straight and in tune (and over a reasonable range of your instrument), you have to apply that knowledge and skill when playing with others. For example, when tuning to the person sitting next to you (who is playing the same note or its octaves or 5ths) or the person opposite you (who is playing the same note or its octaves or 5ths).
Level 3: Playing your note in tune with the chord (where and when possible). You see, it’s not enough to play a note in tune with a tuner or the person next to you. Are you aware that the all-important major 3rd of a chord should be played 10% flat to be in tune? And the 7th of a dominant 7th chord needs to be played 30% flat to be in tune? (Root position chords primarily). This means that the person next to you or opposite you needs to do the same. If this doesn’t happen, then you may have everyone in tune with a particular note but possibly out of tune with the rest of the ensemble. Fascinating, huh!