Can anyone give me any help/advice on getting to know the arpeggios up and down the length of the fretboard? I already know all the notes on the fb well, and I know how the arpeggios are constructed.

Should I be thinking in terms of shapes, notes or scale degrees when playing/figuring out these arps? Anyone got any exercises I can work on?

Well if you get a chord or arpeggio you want to play, figure out the scale degrees and the notes in it etc, then you can just experiment with how you place each note around the neck and how you can voice them on the strings

It should become quite apparent how the strings are all very similar (exept the bottom two, due to the guitar being tuned in 4ths but how they change is easy to realise) and so you'll be able to find placements for them all over the house

Just practicing finding how you can place various chords would serve you very well and it's how I learnt alot of the fretboard a hell of a lot faster than just focusing on what notes on what fret one by one
I assume you mean just the triads (if not, those are the arpeggios you should start

I use mostly shapes. It's fairly easy to do it this way and you probably are already
familiar with some of them -- all your basic major or minor chords already contain
most of them.

I'd first learn them going up & down the neck across groups of 3 strings.
For each inversion there's only 3 shapes to remember. The order will always
be maj - min - min - maj - maj - min - dim in the major scale.

Here's an example of all the shapes on the high 3 strings:

1st inversion

   Maj    Min    Dim

2nd inversion

   Maj    Min    Dim

3rd inversion

   Maj    Min    Dim

The shapes on the other strings are similar -- you just have to account for "B string
half step".

So you just have to go up and down the neck with these shapes through the scale.
On all strings. You can also go across the neck in diatonic 4ths which is good to do.
Keep the scale in mind when you do these. At the end, you will know how to
make 3 different triads (inversions) starting from any note in the scale anywhere
on the neck -- powerfull stuff!

If you want to linearly ascend & descend the scale in triads horizontally, there's
another way of doing it that's very simple, but it relies on knowing/using 3 note
per string fingerings.
^^ I would say to learn the intervals, between each note of the chord and all the other notes in the chord, and then you can choose any order to put them in, and do not have to memorize shapes.
all u really need to know is the location of the tonic
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