Can I transition from past perfect tense to past tense while still referring to the past perfect context?

If I am describing a situation in past tense, then moving into past perfect, can I drop the "hads" so as to use simple past tense verb forms again, but still keep reference to the past perfect context I have created?

Example 1 (with hads):

"I sat down on the bench. As I ate slowly and stared into space, I remembered a time when I had sat in that very same spot. A man had approached me and had asked if he could sit down. I had nodded, and he had sat down. Tears had filled his eyes. He had begun to cry."

The "hads" in this example riddle the prose like botflies. Can I obviate them without savaging the grammar?

Example 2 (reduced hads):

"I sat down on the bench. As I ate slowly and stared into space, I remembered a time when I had sat in that very same spot. A man had approached me and asked if he could sit down. I nodded, and he sat down. Tears filled his eyes. He began to cry."

This example takes advantage of some constructs where I believe that "had" can be dropped, without losing the context.

"A man had approached me and asked if he could sit down." Here the past perfect tense is initiated by "had approached". A second "had" does not appear to be necessary with "asked".

The following sentences "I nodded, and he sat down. Tears filled his eyes." are in simple past and past continuous tenses. But they are betting on the past perfect tense being retained from the prior sentence "A man had approached me and asked if he could sit down." Is this grammatically sound?