mysql: (pdo) continue at last position without using OFFSET - mysql

Question

I wish to retrieve around 200 million profiles using PDO.
It is a partitioned table, so it does not have a primary key, it's sorted with INNODBs internal primary key.
I need to retrieve the data in internal sort order for performance, so using SORT BY some_id and to continue from there would not work for performance reasons.
Using LIMIT OFFSET would not work at all, OFFSET 100 million or more would take ages, the RAM is by far not enough to take all the terrabyte of table data into cache.
I would need something that fetches a chunk of rows, remembers the internal position and continues with next call.
Update
I was digging a bit and the problem seems familiar, it was solved in Oracle by having ROWID and ROWNUM which refer to the internal id.
It seems we have such an id in innodb as well but it's not queryable ?!
That sounds like a significant disadvantage of mysql for performant query.
Table def:
CREATE TABLE `members` (
`id` int(11) NOT NULL DEFAULT 0,
`intern_id` varchar(256) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`first_name` varchar(48) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`last_name` varchar(48) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`middle_name` varchar(48) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`l` varchar(196) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`i` varchar(128) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`ex` varchar(256) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`country_code` varchar(4) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`country_name` varchar(32) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`state_name` varchar(32) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`city_name` varchar(32) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`edu` varchar(256) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`nc` smallint(6) DEFAULT NULL,
`nj` smallint(6) DEFAULT NULL,
`jt` varchar(256) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`cn` varchar(256) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`email_address` varchar(128) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`fpe` tinyint(4) DEFAULT NULL COMMENT '1/0',
`pbu` varchar(256) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`cii` varchar(256) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`unmatched_facts` varchar(2048) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`dt_snapshot` datetime DEFAULT NULL,
`change_small` tinyint(4) DEFAULT NULL,
`change_significant` tinyint(4) DEFAULT NULL,
`jta` varchar(128) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`cna` varchar(128) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`cnia` varchar(256) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`ut_created` int(11) DEFAULT NULL ,
`reserve_int_2` int(11) DEFAULT NULL,
`reserve_vc1` varchar(128) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`reserve_vc2` varchar(128) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
`reserve_vc_3` varchar(256) CHARACTER SET utf8 COLLATE utf8_bin DEFAULT NULL,
KEY `id` (`id`),
KEY `intern_id` (`intern_id`),
KEY `state_name` (`state_name`),
KEY `city_name` (`city_name`),
KEY `i` (`i`),
KEY `country_name` (`country_name`)
) ENGINE=InnoDB DEFAULT CHARSET=latin1
PARTITION BY KEY (`country_name`)
PARTITIONS 30