I made some research regarding your requirement and unfortunately, you can't have 2 VLANs sharing the same network if you want to achieve Inter-VLAN routing. Also, I checked multiple articles/resources regarding accepting double frames on a single interface in SRX and thought of using flexible-vlan-tagging using vlan-id-range but someone mentioned that it is not working for him.
Since you would like to achieve a single connectivity between SRX and Switch, I would recommend to use separate networks for VLAN 10 and VLAN 20.
VLAN 10 - ge-0/0/0.0: 192.168.10.1/24
VLAN 20 - ge-0/0/0.1: 192.168.20.1/24
We can also create irb.10 and irb.20 which you would like to perform initially.
This way we can have better control over the network in terms of scalability. Please let me know if you are facing any challenges with this setup so that we can work on it.