Messages by Google - A simple, helpful text messaging app

I have been running into an apparently known wall. On my verizon android phone, I set gmail to forward what turns into a MMS message to my phone. But the messages arrive out of order and very late, sometimes hours late, and sometimes never.
I was on the verizon forum and apparently it happens and Verizon's response is you have to pay for Enterprise service to get reliable MMS text messaging, which makes a lot of people at least on that thread unhappy.

So I see I do have Google's messaging app installed and use it, AFAIK.
So is there a way to forward a gmail to my phone not using verizon server vzwpix.com?

I was watching the google video and of course they make it look so easy.
Why do I have to use MMS at all using Verizon?

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What I do is I have ContaCam running on my win10 PC
It sends a gmail when it detects motion and includes an animated gif of the motion
Gmail then forwards to my android phone using phonenumber@vzwpix.com

Gmail is reliable, emails come in from Contacam in proper order and within 15 seconds of it finishing rendering the video
Gmail forwards to my phone messaging app. And with Verizon is where the breakdown occurs.

So I was thinking can a google messaging app get a forwarded gmail directly instead of being forced to use the unreliable vzwpix.com. changing to ATT is not an option, people on the afore mentioned thread say ATT handles this with aplomb.

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Top 8 Gmail Notification Settings on Android That You Should Know.

I did see I can set a phone notification to occur when I get a particular gmail in a label (folder), so I set it to do that.
Can the outlook android app notify of new emails by folder when they arrive?

One thing better about outlook app over gmail app is I can click on the picture of the animated gif, and get it to play the video.
Can not do that with gmail.

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The Verizon mail to mms thread where people are complaining it does not work good

Email-to-MMS Not Working Reliably - Verizon Community

Posted for my own future reference