I hope these questions help. They're suggestions of things for you to think about;
don't feel you have to answer them here.

Why do you think it's rude to call in the morning? Do other people tend
to think the same way? How do your customers actually feel about it?
Can you find out by saying things to them like "I didn't want to disturb
you too early in the morning" and see what they say?

What about around 11AM? Would you be able to call then without either
rudeness or tiredness? If so, what about declining any meetings scheduled
for 11AM? "Sorry, I have another commitment then." Or 1:00 PM.

How about taking some time in the morning to lie down for a rest with
your eyes closed, or put your head on your arms on your desk, or
go for a walk in a park etc., so that you'll have energy to call in the afternoon?

How about getting more sleep at night so you'll have more energy during the day?

How about taking a more relaxed mental attitude about meetings, so that
you can attend them without getting as tired?

You can try to think in terms of importance rather than urgency.
In other words: is attending a meeting scheduled for 10 minutes from now
really more important than making a phone call that's one of many
that must be done within about 2 weeks in order for you to make
useful progress in your work?

You can list the expected (and general types of unexpected) meetings for
the upcoming week (e.g. estimate total 5 hours unexpected meetings
of miscellaneous type during the week), order them in order of importance,
decide how much time you want to spend on meetings in total,
and select the highest-priority meetings to attend, (e.g. will attend
total of 3 hours unexpected meetings -- not necessarily the first
ones that come up early in the week! Save some time for
possible more important unexpected meetings later in the week) and send
regrets for the others. If there were two meetings scheduled for the
same time, you would presumably be able to decide quickly which one
is more important for you to attend; you can use that thought process
to sort them and to feel confident to decline them in order to make
calls. And, maybe if you've specifically declined a meeting in order
to make calls, you may be more motivated to actually do a lot of
calls during that time.