Hi Simon,
I see you mention 10Gbit a few times so I'll tackle this from the lower levels - which is often the cause

(And out of scope for normal support)
How is your jumbo frame configuration here? As you mention lan, and iscsi, it's very possible network related, and to be honest the speeds you are mentioning (around 200MB/s) is not close to what's possible on 10Gbit. If it's single jobs on testing and the target are anything above 3x sas disks - you should be pushing 600MB+. (for reference we're running 100GBit around the esxi side, 10Gbit to physical ubuntu IMM Repo's and 40GBit to the backend storage).
When running 10Gbit links with standard mtu size you will still be close to 1Gbit speeds. It's out of scope here as to why - just trust me
First - jumbo frame configuration seems scary, and you should be careful as you don't want to risk cutting yourself off from something, but with a little bit of planning it's actually easy - as jumbo and non jumbo talk no problem (but there are fragmentation on your switches - which could be an issue with very cheap switches) If you are not comfortable with this, or don't manage the switch infrastructure or don't have a network background - ask for somebody that does or reach out.
To test your networking throughput as a first phase (don't worry about disk read/write speeds yet) - use something like iperf. You run it on source or target side in "server" mode - and then on the client you run it connecting to the "server". Run it with multiple streams - say 6 and see what you get. example: "server (10.1.1.2)" : iperf -s " and client (10.1.1.3) " iperf -c 10.1.1.2 -P 6 . You can also reverse the direction to show you if you have issues one way (perhaps duplexing etc) The speeds should be closely matched. This will show you what your switches are capable of.
Second - You have a few places where jumbo frames needs to be configured. Importantly the physical switch ports needs to have it enabled - Vendors differ here, as do switch models, some require it as a global command (which often requires a reboot of the whole switch!! - for example Cisco 2900/ 385x series) - some higher end ones like Nexus can be done "per port". The ports uploading to esx for your data (iscsi) layer needs to be configured, as any other physical ports connecting to the nas. In fact if all your traffic are on 10Gbit I'd recommend jumbo everywhere, but thats a bit out of scope here

You then need to configure your vswitches on esx at one or two places as well, and make sure the switch config -> data ports are mapped correctly. (Often a vswitch has multiple physical uplinks, even 1Gbit and 10Gbit mixed but engineers don't map them correctly) You then need to configure the vnics for any VM's to be jumbo frame enabled as well (In the OS). This is done differently on windows VMs and Ubuntu VMs. For windows VM's you must use vnxnet3 adapters, and there are also a lot of custom powershell tweaking required to allow proper speeds (things like offloading, flow control etc etc). On Linux a bit less tweaking - more a challenge as most flavours differe WHERE to change mtu, and also how to save it so a reboot don't reset to standard. You then lastly have to make sure jumbo frames are also enabled on the physical ports on the NAS.
You can then repeat the tests with iperf and see the difference.
Simple method to test jumbo frames end to end is with say 2x vm's running via the switch. Simply ping one from the other, but add " -l 8900 and -f" ("dash Lima dash Foxtrot) so example from: 10.1.1.2 : from 10.1.1.2: ping 10.1.1.3 -l 8900 -f It means ping with mtu size 8900 (jumbo is >9000 but you leave a few bits for overhead) and -f is "don't defrag packets" -so force 8900 - otherwise it might seem to work but isn't really using jumbo! If everything checks out you are ready to go and should see great improvements.
Just on a last note - you mentioned the "processing speed" as a metric - please note this is not a reflection of actual writing speeds through the network - it's merely a calculation of time it took to read data + write changed blocks - many other factors play a role here. I have jobs with processing speeds of 2-3Gbits/s but actual writing speeds are around 1GB. (the 10Gbit max).