After successful testing of the @hellbondz's method, I found that my second network interface in the DSM is inaccessible from my LAN (I use multi-homed network).
This was happened because:
Without this script PVE will add both netdev into default bridge - vmbr0 (a public bridge in my case).
I patched two PVE scripts to be able add network interface with Proxmox GUI and staying out from edit config manually (what somebody can't do it correctly).
So my method of using Network Driver Intel e1000e with Proxmox, which required to be able upgrade to the the latest DSM version (current up to DSM 6.2.2-24922 Update 2) and keep network worked:
1) Make DSM VM backup as usual!
2) Make PVE scripts backup:
cp /usr/share/perl5/PVE/QemuServer.pm /usr/share/perl5/PVE/QemuServer.pm.default
cp /usr/share/pve-manager/js/pvemanagerlib.js /usr/share/pve-manager/js/pvemanagerlib.js.default
3.1) Open /usr/share/perl5/PVE/QemuServer.pm
find needed block with keyword 'e1000 (or 'vmxnet3' - less results than for '1000')
replace:
my $nic_model_list = ['rtl8139', 'ne2k_pci', 'e1000', 'pcnet', 'virtio',
'ne2k_isa', 'i82551', 'i82557b', 'i82559er', 'vmxnet3',
'e1000-82540em', 'e1000-82544gc', 'e1000-82545em'];
to (add 'e1000e'):
my $nic_model_list = ['rtl8139', 'ne2k_pci', 'e1000', 'e1000e', 'pcnet', 'virtio',
'ne2k_isa', 'i82551', 'i82557b', 'i82559er', 'vmxnet3',
'e1000-82540em', 'e1000-82544gc', 'e1000-82545em'];
3.2) Open/find/replace /usr/share/pve-manager/js/pvemanagerlib.js
if ((match_res = p.match(/^(ne2k_pci|e1000|e1000-82540em|e1000-82544gc|e1000-82545em|vmxnet3|rtl8139|pcnet|virtio|ne2k_isa|i82551|i82557b|i82559er)(=([0-9a-f]{2}(:[0-9a-f]{2}){5}))?$/i)) !== null) {
res.model = match_res[1].toLowerCase();
to:
if ((match_res = p.match(/^(ne2k_pci|e1000|e1000e|e1000-82540em|e1000-82544gc|e1000-82545em|vmxnet3|rtl8139|pcnet|virtio|ne2k_isa|i82551|i82557b|i82559er)(=([0-9a-f]{2}(:[0-9a-f]{2}){5}))?$/i)) !== null) {
res.model = match_res[1].toLowerCase();
next replace block:
Ext.define('PVE.form.NetworkCardSelector', {
extend: 'Proxmox.form.KVComboBox',
alias: 'widget.pveNetworkCardSelector',
comboItems: [
['e1000', 'Intel E1000'],
['virtio', 'VirtIO (' + gettext('paravirtualized') + ')'],
['rtl8139', 'Realtek RTL8139'],
['vmxnet3', 'VMware vmxnet3']
]
});
to:
Ext.define('PVE.form.NetworkCardSelector', {
extend: 'Proxmox.form.KVComboBox',
alias: 'widget.pveNetworkCardSelector',
comboItems: [
['e1000', 'Intel E1000'],
['e1000e', 'Intel e1000e'],
['virtio', 'VirtIO (' + gettext('paravirtualized') + ')'],
['rtl8139', 'Realtek RTL8139'],
['vmxnet3', 'VMware vmxnet3']
]
});
4) Run 'service pveproxy restart' and reload PVE admin interface - you will be able to change the Network driver of your DSM VM from e1000 to e1000e.
5) Save copies of edited scripts to somewhere else to be able restore/compare scripts versions after Proxmox upgrades.
Again - make backups before run any test from my tutorial.
Good luck