After a lot of research, I finally figured out how to enable the E7440's touchscreen in macOS Catalina and Big Sur. No DSDT patches or programs are required to make it function. In Opencore, you need to add the main VoodooI2C kext, and it's satellite VoodooI2CHID. After you added your kexts to the folder, you then need to add the following arguments related to VoodooI2C and VoodooI2CHID:
<dict>
<key>BundlePath</key>
<string>VoodooI2C.kext/Contents/PlugIns/VoodooI2CServices.kext</string>
<key>Comment</key>
<string>I2C trackpad logging</string>
<key>Enabled</key>
<true/>
<key>ExecutablePath</key>
<string>Contents/MacOS/VoodooI2CServices</string>
<key>MaxKernel</key>
<string></string>
<key>MinKernel</key>
<string></string>
<key>PlistPath</key>
<string>Contents/Info.plist</string>
</dict>
<dict>
<key>BundlePath</key>
<string>VoodooI2C.kext/Contents/PlugIns/VoodooGPIO.kext</string>
<key>Comment</key>
<string>I2C trackpad GPIO controller</string>
<key>Enabled</key>
<true/>
<key>ExecutablePath</key>
<string>Contents/MacOS/VoodooGPIO</string>
<key>MaxKernel</key>
<string></string>
<key>MinKernel</key>
<string></string>
<key>PlistPath</key>
<string>Contents/Info.plist</string>
</dict>
<dict>
<key>BundlePath</key>
<string>VoodooI2C.kext</string>
<key>Comment</key>
<string>I2C trackpad</string>
<key>Enabled</key>
<true/>
<key>ExecutablePath</key>
<string>Contents/MacOS/VoodooI2C</string>
<key>MaxKernel</key>
<string></string>
<key>MinKernel</key>
<string></string>
<key>PlistPath</key>
<string>Contents/Info.plist</string>
</dict>
<dict>
<key>BundlePath</key>
<string>VoodooI2CHID.kext</string>
<key>Comment</key>
<string>I2C trackpad satellite</string>
<key>Enabled</key>
<true/>
<key>ExecutablePath</key>
<string>Contents/MacOS/VoodooI2CHID</string>
<key>MaxKernel</key>
<string></string>
<key>MinKernel</key>
<string></string>
<key>PlistPath</key>
<string>Contents/Info.plist</string>
</dict>
<dict>
<key>BundlePath</key>
<string>VoodooI2C.kext/Contents/PlugIns/VoodooInput.kext</string>
<key>Comment</key>
<string>Multitouch engine</string>
<key>Enabled</key>
<true/>
<key>ExecutablePath</key>
<string>Contents/MacOS/VoodooInput</string>
<key>MaxKernel</key>
<string></string>
<key>MinKernel</key>
<string></string>
<key>PlistPath</key>
<string>Contents/Info.plist</string>
</dict>
VoodooI2C and VoodooI2CHID should be enough to enable all USB-HID touchscreens when using Opencore. Unfortunately, I was not able to get these kexts working in Clover due to it's less precise kext injection. Anyway, I'll share my E7440's Opencore 0.6.2 config. It's a bit messy, but it works. It should (in theory) work with macOS Big Sur, but I have not tested it yet. Before using this config, make sure to generate a new system serial number, a new system UUID, and a new system MLB under PlatformInfo.