Explicitly set ROWNUM in column - sql

Question

I'm trying to split what was a large table update into multiple inserts into working tables. One of the queries needs uses the row number in it. On an INSERT in oracle, can I explicitly add the ROWNUM as an explicit column? This is a working table ultimately used in a reporting operation with a nasty partion over clause and having a true row number is helpful.
create table MY_TABLE(KEY number,SOMEVAL varchar2(30),EXPLICIT_ROW_NUMBER NUMBER);
INSERT /*+PARALLEL(AUTO) */ INTO MY_TABLE(KEY,SOMEVAL,EXPLICIT_ROW_NUMBER) (
SELECT /*+PARALLEL(AUTO) */ KEY,SOMEVAL,ROWNUM
FROM PREVIOUS_VERSION_OF_MY_TABLE
);
where PREVIOUS_VERSION_OF_MY_TABLE has both a KEY and SOMEVAL fields.
I'd like it to number the rows in the order that the inner select statement does it. So, the first row in the select, had it been explicitly run, would have a ROWNUM of 1, etc. I don't want it reversed, etc.
The table above has over 80MM records. Originally I used an UPDATE, and when I ran it, I got some ORA error saying that I ran out of UNDO space. I do not have the exact error message at this point anymore.
I'm trying to accomplish the same thing with multiple working tables that I would have done with one or more updates. Apparently it is either hard, impossible, etc to add UNDO space, for this query (our company DB team says), without making me a DBA, or spending about $100 on a hard drive and attaching it to the instance. So I need to write a harder query to get around this limitation. The goal is to have a session id and timestamps within that session, but for each timestamp within a session (except the last timestamp), show the next session. The original query is included below:
update sc_hub_session_activity schat
set session_time_stamp_rank = (
select /*+parallel(AUTO) */ order_number
from (
select /*+parallel(AUTO) */ schat_all.explicit_row_number as explicit_row_number,row_number() over (partition by schat_all.session_key order by schat_all.session_key,schat_all.time_stamp) as order_number
from sc_hub_session_activity schat_all
where schat_all.session_key=schat.session_key
) schat_all_group
where schat.explicit_row_number = schat_all_group.explicit_row_number
);
commit;
update sc_hub_session_activity schat
set session_next_time_stamp = (
select /*+parallel(AUTO) */ time_stamp
from sc_hub_session_activity schat2
where (schat2.session_time_stamp_rank = schat.session_time_stamp_rank+1) and (schat2.session_key = schat.session_key)
);
commit;