Should smtp_helo_name always be the same as your MX record?

Question

I can't seem to satisfy HELO checks on SPF records in all cases. I have an SPF record for my domain like this:

"v=spf1 mx -all"

The MX records in the zone are:

mx0.mydomain.org.uk.          3600 IN A         1xx.xx.xx.59
mx0.mydomain.org.uk.          3600 IN AAAA      2001:xxx:x:xxx::3b
mx1.mydomain.org.uk.          3600 IN A         2xx.xx.xxx.201
mx1.mydomain.org.uk.          3600 IN AAAA      2a03:xxx:xx:xxx::2 

The HELO name of my sending server is mydomain.org.uk.

I can get HELO to pass with the above SPF record:

SPF helo    header      Received-SPF: 

pass (mydomain.org.uk: 1xx.xx.xx.59 is authorized to use 'mydomain.org.uk' in 'helo' identity (mechanism 'mx' matched)) 

receiver=ts11-do.checktls.com; identity=helo; helo=mydomain.org.uk; client-ip=1xx.xx.xx.59

However, some checkers don't like this and say they can't find an A record for the sender mydomain.org.uk. But if I change the HELO to mx0.mydomain.org.uk I then get a fail because of "no applicable sender policy available":

SPF helo    header      Received-SPF: 

none (mx0.mydomain.org.uk: No applicable sender policy available) receiver=ts11-do.checktls.com; identity=helo; helo=mx0.mydomain.org.uk; client-ip=1xx.xx.xx.59

SPF helo    local       mx0.mydomain.org.uk: No applicable sender policy available

How can I satisfy both checks?