I really like the 6 steps of paraphrasing, esp. the one that asks students to check for the presence of all the essential information. When I taught a paraphrasing lesson, I realized some students did not have all the essential information although they did a good job in changing the word form or sentence structure. Therefore, I think it's a good idea to incorporate that step. Somewhat similar to the 6 steps you use, what I did in class was as follows,
1. Ask students to form in groups of 3.
2. Give each student in a group a different text (it's usually a short paragraph because students' levels are intermediate.) and then give them a couple minutes to read their text.
3. Ask them to cover up the printed handout or minimize the window if the handout is an online document.
4. Students need to verbally paraphrase what they have just read to their groups.
5. Then they will be given time to write down what they have just paraphrase in a new document.
6. Go back to the original texts and check for the presence of all the essential information.
Extension to the activity: Ask students to post their paraphrased texts on a GoogleDoc and then group the students who read the same text. Teachers can give students some time to discuss what strategies they used to paraphrase the text, and then elicit answers from students. Afterwards, teachers can challenge students to peer review a different group's responses and nominate the best paraphrase. As students give their answers, teachers can ask students to justify their choices before giving a mini lecture on how to paraphrase. After the lecture, students can go back to and revise their original paraphrase.
This type of strategy can also be used to teach a summary lesson. An alternative way to ask students to peer review each other's response is to let them walk around and read people's summary. That would help ease students' boredom if the class is a 80-min class.
Some exercises I used were found on Purdue OWL. It's pretty good that they have exercises for different levels of students. Details can be seen the following link https://owl.english.purdue.edu/exercises/32/41/77