I also have a large/old gold nugget tree which finishes with ripe fruit about now. My gold nugget tastes good til the end (mid-June).
But there is another mandarin that hangs longer, it's a murcott mandarin. I have two versions of the murcott tree which has different fruits/tastes. The ones that hang on the tree ripe until July is the murcott (honey, from FL) with super thin, smooth skin, has many seeds, and is very sweet. When you compare the taste of the fruits in May-June with gold nugget the murcott is much sweeter and juicier. I'll pick a few ripe fruits tomorrow and post it so you can see what the murcott fruit looks like. Of all my mandarins, it is the only one that is still ripening now (March-July?). The fruit skin is so thin and tightly adheres on the flesh, so it is not as easy to peel but it does still peel away from the flesh sacks. This murcott variety closely matches the UCR CCPP VI-147. My other murcott (VI-462) fruits are different. It has very few seeds, peels easily, but doesn't hold until June. The VI-462 ripens from Jan-Apr/May. It tastes more watery and not as sweet as the VI-147.
Yes, I agree, I have four varieties of Valencia orange and they do stay ripe and hang on the tree during summer. They are good for juicing, messy if you try to peel and eat it, very juicy. If I had to choose between the murcott and valencia orange, I would pick the valencia orange since it has less seeds, fruits are larger, so you get more to eat.