Thank you, everyone, for your concerns about the furnace.
I called the furnace company a few minutes after 8:00 a.m. and told them that the furnace was still malfunctioning. They promised to have a technician out between 12:00 p.m. and 2:00 p.m.
The same technician who was here yesterday arrived a little after 12:00 p.m. My daughter, who was between online meetings (she has four meetings scheduled for today) was able to show the video she took of the furnace to him.
He tried to tell us that that is how it is supposed to be! What? With a flame shooting out due to delayed ignition? He said the pilot light flame was set at normal, right now (or, maybe it was set too low and he didn't want to admit it!), but, it takes a little time for the flame to ignite the gas and that's what is causing the flame. Yes, we know; delayed ignition. That was the reason why the gas company technician red tagged the old furnace in the first place!
He then said we had two options - we could either increase the pilot light flame or leave it as it is! According to him, a lot of customers complain if the flame is increased because of the noise (and, probably, more gas consumed by the pilot light?), but, it speeds up the process of lighting the furnace burners.
My daughter and I chose the 'increase the pilot light flame' option! We prefer increased noise and higher gas bills to flames shooting out when the furnace is turned on! My goodness! I'll find another way to toast those marshmallows, not that anyone had any to share with me, anyway! LOL!
So, he increased the pilot light flame and we tried turning the furnace on a couple of times and it worked well, each time. I suppose the real test will come tonight, when we turn the furnace on! I can hear the pilot light if I am standing right next to the furnace and listening for it, but, it's not that loud!
Now, the task will be to let the gas company technician, who is scheduled to come out to check it, tomorrow, know that the pilot light is set on a higher setting on purpose and ask him not to turn it down!
Hopefully, that is the end of this furnace saga!