Hi Luke
I think you need to start very simply. I am assuming you have been trying to learn to improvise by practicing notated licks and notated solos. This will not help you very much at this stage, because all you will try to do is insert them or play them from memory, which is not what improvisors do. If you think of how you have a conversation with someone, neither of you write down or prepare what you are going to say before you meet. You are spontaneous, you might make a few mistakes as you are speaking but you react to what is happening (what they are saying) and respond with your reply.

In soloing, you are listening to what you are playing (also what the backing musicians are playing) and constructing a lovely solo over time, connecting bits, flowing things on from one to the other and making some kind of integrated sense of the notes and phrasing (like when you are speaking to someone using words.) It is kind of 'musical speech.'

I would start with a few simple tunes. If you are coming to jazz, here are a few:
Summertime
Satin Doll
Autumn leaves
Blues changes (using simple chords)
Footprints
Maiden Voyage

Choose a couple to work with.
Play them at a slow tempo. You mentioned tripping over the changes. If it is a ballad tempo it is much easier. Remember you are in charge of the solo, there is no hurry, so when you do not know what note to play, give your solo a rest (kind of like a breath) and start up again when you have another idea. With a ballad you can play long notes and create gorgeous melodies that do not have to be fast. Good to work on tone of the notes with the ballads of course (you will know this from your classical guitar studies.)
Remember that a note you are playing might just as well be part of the following chord change so it can stay there playing it letting it ring out until you sort out where it is going next, if it is not, then you only have to move up/down a fret or two and play the new note that will fit inside the new chord.
Listen all the time to the musical phrasing licks you are doing as you are playing. This is your feedback. Each note is precious and leads to the next and the next. Take an idea (rhythmic or intervallic) and expand that idea for the next bit. You do not have to keep on coming up with new ideas or new licks each time. Think temporally and develop your solo temporally so each bit can relate to the next (of course every now and again you will want a new idea, but this is a way to start.... you already have the previous lick to relate the next to.)

Put away your notation notes, notated licks and solos (sounds like you know how to get around your instrument.) You know scales so you know the kind of notes to use with a chord, but you would know that a solo is not scales nor arppegios. They only give you an idea of what notes to use as a starting point. So start on a note that the first chord suggests, let it breathe, then add another then another. Ballads remember. Each note has its own (sounding) identity as to where it is in the chord (chord-scale) that is being played by the rhythm section or inside the song. Your ear needs to get used to this and will very gradually start knowing what each note will sound like against (within) the chord. This is happening as you play slow ballads, as are many other things. You need to start slowly to build up your improvising skills - aural, finger positioning, listening, etc.

Modal tunes are good to start with as the chords do not change too much and you can linger in the chord sounds and notes for longer without getting muddled as the chords change each bar. (The last two listed are modal.) And you can practice the licks YOU are coming up with against (within) the chords that are going by as the piece is happening (either backing play-alongs or in your head as you are counting through it.) Do not be afraid to stop and practice a little lick you came up with. Enjoy it, get it down under your fingers. With modal tunes it is easier to do this with if you are using play-along backings.

You need to start slowly (and enjoy it). Listen to ballad playing of your favorite players. If you cannot solo slowly, you will not be able to do it faster.

Let us know how you are progressing. Best wishes.