Hi gamber,
according to this documentation, your switch is able to handle 802.1 Q VLANs, which includes only tagged VLANs for my understanding.
http://h20566.www2.hpe.com/hpsc/doc/public/display?sp4ts.oid=7533927&docId=emr_na-c04808248&docLocale=en_US
On Page 5 you will find this restriction, your switch won't support Management Interface other than VLAN 1 or default VLAN.
As for VLAN interfaces, the switch supports only VLAN-interface 1,and the VLAN-interface cannot
be modified.
The only ways to solve your problem, seems to me:
1.) disable VLANs and reduce your 2510 switch port to an access port only with Default VLAN 1
2.) use VLAN1 as default untagged VLAN in your 2510 switch trunk port and manage routing to VLAN 1 from it by setting up a VLAN interface for VLAN 1.
3.) install a management system as an extra hop with access to VLAN 1 and the management VLAN.
4.) buy a bigger switch.
Btw: I am neither experienced with a 2510, nor with a 1620. There might be better solutions.